{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "62865dd9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Probabilités et Statistique \n",
    "Cours 1/3\n",
    "\n",
    "Dimitri de Smet d'Olbecke"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9f523e00",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set_context('talk')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "153d1bed-6641-4b77-9cca-8a57b6becee9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Plan\n",
    "- Introduction\n",
    "- Variable Aléatoire\n",
    "- Principes de probabilités\n",
    "- Quelques distributions\n",
    "- Espérance mathématique\n",
    "- Estimateurs d'une distribution\n",
    "- Distributions multivariées\n",
    "- Probabilités conditionnelles\n",
    "- Probabilité marginale\n",
    "- Régressions\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3799d01",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Probabilités et Statistiques\n",
    "\n",
    "- Probabilités : \n",
    "    - Branche des mathématiques qui étudie les phénomènes aléatoires \n",
    "    - Calcul les \"chances\" de survenue d'un évènement\n",
    "- la statistique\n",
    "    - Disciplines qui étudient les phénomènes à travers \n",
    "        - la collecte de données\n",
    "        - leur traitement\n",
    "        - leur analyse\n",
    "        - l'interprétation des résultats\n",
    "        - leur présentation\n",
    "- statistiques (pl.) :\n",
    "    résultat d'une suite d'opérations appliquées à un ensemble de nombres appelé échantillon. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74256b50",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Probabilités et Statistiques\n",
    "\n",
    "\"Parmi les thèmes à propos desquels les statisticiens ne sont pas d'accord, se trouve la définition de leur science.\"\n",
    "\n",
    "― Maurice Kendall, 1935\n",
    "\n",
    "Retenons à ce stade :\n",
    "- Probabilités + Statistique : Les sciences du hasard"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "327de9e0-48cb-4da8-8e1f-a77b09ab168c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Intérêt des sciences du hasard\n",
    "\"It's tough to make predictions, especially about the future.\"\n",
    "― Yogi Berra"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a92825a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Intérêt des sciences du hasard\n",
    "(dans les entreprises)\n",
    "- Que peut-on apprendre des données ?  \n",
    "- Quelles prédictions permettent-elles ? \n",
    "- Avec quel degré de certitude ? \n",
    "- Quels gains de productivité peuvent-elle amener ? \n",
    "- Peuvent-elles nous aider à mieux cerner des utilisateurs ou des clients ?\n",
    "- Minimiser la part d'incertitudes sur l'avenir."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "490058e6-bae8-4d5d-a2b5-07422bf75ed4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Intérêt des sciences du hasard\n",
    "(en ce qui vous concerne)\n",
    "- Explosion des volumes de données\n",
    "- Retombées économiques\n",
    "- Part grandissantes dans les métiers de l'informatique\n",
    "- Mener à bien son projet de passerelle"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97b06910-e937-4b95-8689-888bbfcf6ca2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Statistique\n",
    "- Rappels\n",
    "    - Moyenne\n",
    "    - Médianne\n",
    "    - Mode\n",
    "    - Écart-type\n",
    "    - Quartile\n",
    "- Calculs avec le jeu de données sur l'ozone (température à Sandburg en °C)\n",
    "    - Réimplémentez les fonctions, vérifiez avec numpy.mean(), numpy.median(), ...\n",
    "    - Dressez les diagrammes suivants \n",
    "        - boite à moustache (boxplot)\n",
    "        - histogramme\n",
    "        - histogramme cumulé"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "291eba3b",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import json\n",
    "df = pd.read_csv('data/data.csv')\n",
    "with open('data/variables.json', 'r') as f:\n",
    "    names = json.load(f)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c5f5b559",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "92.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts = df.tS.dropna().values\n",
    "import numpy as np\n",
    "np.quantile(q=0,a=ts)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.boxplot(ts);\n",
    "np.percentile(q=99,a=ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b7ad5213",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['month',\n",
       " 'day_of_month',\n",
       " 'day_of_week (1=Monday)',\n",
       " 'ozone [pphm]',\n",
       " '500 millibar pressure height (m) measured at Vandenberg AFB',\n",
       " 'Wind speed (mph) at Los Angeles International Airport (LAX)',\n",
       " 'humidity (%) at LAX',\n",
       " 'temp. Sandburg [F]',\n",
       " 'temp.  El Monte [F]',\n",
       " 'Inversion Base Height (feet)',\n",
       " 'Pressure gradient (mm Hg) from LAX to Daggett, CA',\n",
       " 'Inversion base temperature (degrees F) at LAX',\n",
       " 'Visibility measured at LAX [miles]']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f0b90a4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exemple 1D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "75e85db7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Taille d'une population en cm\n",
    "x = np.random.normal(size=int(10e6),loc=179,scale=8)\n",
    "plt.hist(x,bins=50);\n",
    "plt.grid()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "735edbb3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.ticker import PercentFormatter\n",
    "plt.hist(x,bins=50, weights=np.ones(len(x)) / len(x))\n",
    "plt.grid()\n",
    "\n",
    "plt.gca().yaxis.set_major_formatter(PercentFormatter(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d267b32a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.ticker import PercentFormatter\n",
    "\n",
    "plt.hist(x,bins=100, weights=np.ones(len(x)) / len(x),cumulative=1)\n",
    "plt.grid()\n",
    "\n",
    "\n",
    "plt.gca().yaxis.set_major_formatter(PercentFormatter(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f80cd5d2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "179.00757425195704\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.ticker import PercentFormatter\n",
    "plt.hist(x,bins=100, weights=np.ones(len(x)) / len(x),cumulative=1,alpha=0.7)\n",
    "plt.grid()\n",
    "plt.gca().yaxis.set_major_formatter(PercentFormatter(1))\n",
    "plt.plot([120,np.median(x)],[50e-2,50e-2],'k');plt.plot([np.median(x),np.median(x)],[50e-2,0],'k')\n",
    "print(np.median(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aaaf47d2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# loi normal\n",
    "from scipy import stats\n",
    "x = np.linspace(120,220,num=100)\n",
    "y = stats.norm.pdf(x,179,8)\n",
    "plt.plot(x,y);plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2b5f1bce",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = stats.norm.cdf(x,179,8);\n",
    "plt.plot(x,y);plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e45e93bf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exemple 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "014a3cfc",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1b08443e4a0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.random.multivariate_normal(mean=[179,75],cov = [[8,4],[4,8]],size=1000)\n",
    "plt.scatter(X[:,0],X[:,1],alpha=1,s=2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "32485ab1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist2d(X[:,0],X[:,1],bins=50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "57d92fc1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Create grid and multivariate normal\n",
    "x = np.linspace(160, 190, 200) # Create a mesh of 200 x-points\n",
    "y = np.linspace(65, 85, 200) # Create a mesh of 200 y-points\n",
    "\n",
    "X, Y = np.meshgrid(x,y)\n",
    "pos = np.dstack((X, Y))\n",
    "Z = stats.multivariate_normal.pdf(pos,[179,75],[[8,4],[4,8]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "74022ef5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.figure(figsize=[5,10]).add_subplot(projection='3d')\n",
    "# Plot the 3D surface\n",
    "ax.plot_surface(X, Y, Z, edgecolor='royalblue', lw=0.5, rstride=8, cstride=8,\n",
    "                alpha=0.1)\n",
    "ax.set(ylim=(65, 85), xlim=(160, 190), zlim=(0, 0.03),\n",
    "       xlabel='X', ylabel='Y', zlabel='Z');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9db6bd2d-f0f4-4e03-aec6-bf0cf41ecebb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Variable Aléatoire\n",
    "- Variable dont la valeur est déterminée après la réalisation d’un phénomène, expérience ou événement, aléatoire\n",
    "- Notation en majuscule $X$, $Y$, $Z$ (souvent celles-là)\n",
    "- Elle est associée à des probabilités $\\mathbb  {P}_X$ d'évènements $A$, $B$, $C$, ... :  \n",
    " $\\mathbb  {P}_X(A)$, $\\mathbb  {P}_X(B)$, $\\mathbb  {P}_X(C)$ (souvent $A$, $B$, $C$, ... ou $A_1$, $A_2$, $A_3$, ...)\n",
    "- L'ensemble des évènements possible est $\\Omega$\n",
    "- $A,B,C \\in \\Omega$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dc78d13-a354-467d-8304-958f215a5dfa",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Exemples\n",
    "- Discret : Jeux de hasard (cartes, dés, pile ou face)\n",
    "- Continu : Prédiction continue (météo, ratings, effet d'un médicament, ventes, ...)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0693537c-7993-4a0d-9ecf-81dc7e02bf6d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Quelques principes de probabilité\n",
    "- $0\\leq \\mathbb  {P}(A)\\leq 1$\n",
    "- $\\mathbb  {P}(\\Omega) = 1$\n",
    "\n",
    "Évènements incompatibles :\n",
    "- ${\\mathbb  {P}}(A_{1}\\cup A_{2}\\cup \\cdots )=\\sum _{{i=1}}^{{+\\infty }}{\\mathbb  {P}}(A_{i})$\n",
    "\n",
    "Évènements compatibles :\n",
    "- ${\\mathbb  {P}}(A_{1}\\cup A_{2})={\\mathbb  {P}}(A_{1}) + \\mathbb  {P}(A_{2})- \\mathbb  {P}(A_1\\cap A_2)$\n",
    "\n",
    "Évènements Indépendants :\n",
    "- ${\\mathbb  {P}}(A_{1}\\cap A_{2})={\\mathbb  {P}}(A_{1}) \\times \\mathbb  {P}(A_{2})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd636f19-179f-4800-a5ba-b22137a1a419",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Loi des Grands Nombres\n",
    "~ Les propriétés d'un échantillon tendent vers les propriétés de la distribution de probabilité qui la gouverne.\n",
    "\n",
    "$\\rightarrow$ Fait le pont entre les statistiques et les probabilités"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b7d831-ba13-44a0-85ff-f40aa53c6f95",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Lois de probabilité classiques\n",
    "## Discrète uniforme : $\\frac{\\# cas\\, favorables}{\\# cas\\, possibles}$\n",
    "- $A_1$ : Tirer un valet de trèfle dans un paquet de 52 cartes\n",
    "- $A_2$ : Obtenir un 6 au dé\n",
    "- $A_3$ : Obtenir deux 6 sur deux lancers de dé\n",
    "- $A_4$ : Obtenir au moins un 6 sur deux lancers de dé\n",
    "- $A_5$ : Obtenir au moins un 6 sur six lancers de dé\n",
    "- $A_6$ : Obtenir 4 fois \"face\" en quatre lancers de pièce\n",
    "- $A_7$ : Obtenir \"face\" après avoir obtenu 3 fois \"piles\"\n",
    "- $A_8$ : Obtenir exactement deux 6 sur cinq lancers de dé"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a5cbac6-7d84-47d9-9d5b-98baa73541a8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Lois de probabilité classiques\n",
    "## Binomiale  \n",
    "- modélise la fréquence du nombre de succès obtenus lors de la répétition de plusieurs expériences aléatoires identiques et indépendantes.\n",
    "- $\\frac{\\# cas favorables}{\\# cas possibles}$\n",
    "- $p$ : chance de succès sur une expérience\n",
    "- ${\\displaystyle \\mathbb {P} (X=k)={n \\choose k}\\,p^{k}(1-p)^{n-k}}$\n",
    "- ${n \\choose k}=C_{n}^{k}\\,={\\frac  {n!}{k!(n-k)!}}.$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99259b9c-7285-492c-abef-66c86e74356b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "- Aux dés, sur cinq lancers, le nombre de combinaisons dans lequelles il y a deux 6 est ${5 \\choose 2}=C_{5}^{2}\\,={\\frac  {5!}{2!(5-2)!}}=10.$\n",
    "    1. 6,6,x,x,x\n",
    "    1. 6,x,6,x,x\n",
    "    1. 6,x,x,6,x\n",
    "    1. 6,x,x,x,6\n",
    "    1. x,6,6,x,x\n",
    "    1. x,6,x,6,x\n",
    "    1. x,6,x,x,6\n",
    "    1. x,x,6,6,x\n",
    "    1. x,x,6,x,6\n",
    "    1. x,x,6,x,6\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "73fbd978-7588-485e-a925-33138dc548c7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "math.comb(5,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98017229",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Binomiale\n",
    "Quelle est la probabilité d'obtenir deux 6 sur 5 lancés de dé?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53d0e25a-9380-4dd5-9905-7c2ee5f5f857",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "- ${n \\choose k}\\,p^{k}(1-p)^{n-k} = 10\\times(\\frac{1}{6})^2\\times (\\frac{5}{6})^3 = 0.16075$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23bd1111-e8cc-41b5-8c05-9e2a51bc79d8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Loi binomiale : Expériences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fa1470b3-3e14-4936-b060-5de2d0d9ee39",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "np.random.seed(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "52910921-0915-4313-8e1d-3c6d67112824",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 6 1 4 3]\n",
      " [4 1 3 2 4]\n",
      " [6 3 5 5 5]\n",
      " [6 4 5 3 4]\n",
      " [4 3 2 3 5]\n",
      " [4 6 1 5 4]\n",
      " [2 3 1 5 5]\n",
      " [3 5 3 2 1]\n",
      " [3 6 3 2 6]\n",
      " [1 2 1 3 6]]\n",
      "0.1\n"
     ]
    }
   ],
   "source": [
    "N = 10\n",
    "x = np.random.randint(1,7,[N,5])\n",
    "print(x)\n",
    "print(sum(np.sum(x == 6,axis=1)==2)/N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b789b425-05c8-40fe-9394-57e1d8c27acd",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "## Loi binomiale : Expériences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d58f5993-6757-4d72-81ba-3237c3c32b02",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 2 2 5 3]\n",
      " [4 1 4 1 3]\n",
      " [3 1 5 3 1]\n",
      " ...\n",
      " [6 4 5 5 4]\n",
      " [5 4 1 5 6]\n",
      " [5 5 4 2 1]]\n",
      "0.160558\n"
     ]
    }
   ],
   "source": [
    "N = 1000000\n",
    "x = np.random.randint(1,7,[N,5])\n",
    "print(x)\n",
    "print(sum(np.sum(x == 6,axis=1)==2)/N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f4043a5-45a4-486e-a8d1-c0ea722f92af",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "## Loi binomiale vs Expériences\n",
    "### Nombre de 6 sur 20 lancés"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "fd5d3ab5-302a-4b5a-bca5-05ae7ec068cb",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "x = np.random.randint(1,7,[N,20])\n",
    "\n",
    "plt.figure(figsize=[15,5])\n",
    "plt.hist(np.sum(x == 6,axis=1),weights=np.ones(N)/N,bins=np.linspace(0,12,13),label='expriences');\n",
    "n = np.array(range(13))\n",
    "plt.bar(n,[math.comb(20,n_i)*(1/6)**n_i*(5/6)**(20-n_i) for n_i in n],color='orange',label='loi binomiale')\n",
    "plt.grid()\n",
    "plt.title('Nombre de 6 sur 20 lancés ({} exp.)'.format(N))\n",
    "plt.xlabel(\"nombre de 6\")\n",
    "plt.ylabel(\"Fréquence d'occurance\")\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38fdc153-7fd3-466a-904c-22179d02c4a5",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "## Loi binomiale vs Expériences\n",
    "### Nombre de 6 sur 20 lancés"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4b07e2c0-c58c-4173-b3f9-a75abc812bd1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IAAAAAAAAWACFQAAAAAAAAMACKAQCAAAAAAAAFkAhEAAAAAAAALAACoEAAAAAAACABVAIBAAAAAAAACyAQiAAAAAAAABgARQCAQAAAAAAAAugEAgAAAAAAABYAIVAAAAAAAAAwAIoBAIAAAAAAAAWQCEQAAAAAAAAsID/B7sC4bAq4lsFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "x = np.random.randint(1,7,[N,20])\n",
    "plt.figure(figsize=[15,5])\n",
    "plt.hist(np.sum(x == 6,axis=1),weights=np.ones(N)/N,bins=np.linspace(0,12,13),label='expriences');\n",
    "n = np.array(range(13))\n",
    "plt.bar(n,[math.comb(20,n_i)*(1/6)**n_i*(5/6)**(20-n_i) for n_i in n],color='orange',label='loi binomiale')\n",
    "plt.grid()\n",
    "plt.title('Nombre de 6 sur 20 lancés ({} exp.)'.format(N))\n",
    "plt.xlabel(\"nombre de 6\")\n",
    "plt.ylabel(\"Fréquence d'occurrence\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b614d35-8567-4d87-8224-f5031329c587",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "## Pile ou face sur 100 lancés"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e115f396-4580-4f0e-9568-582b74b743c4",
   "metadata": {
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100000\n",
    "x = np.random.randint(1,3,[N,20])\n",
    "plt.figure(figsize=[15,5])\n",
    "plt.hist(np.sum(x == 1,axis=1),weights=np.ones(N)/N,bins=np.linspace(0,20,21),label='expriences');\n",
    "n = np.array(range(20))\n",
    "plt.bar(n,[math.comb(20,n_i)*(0.5)**n_i*(0.5)**(20-n_i) for n_i in n],color='orange',label='loi binomiale')\n",
    "plt.grid()\n",
    "plt.title(\"Nombre de 'faces' sur 100 lancés ({} exp.)\".format(N))\n",
    "plt.xlabel(\"nombre de 'faces'\")\n",
    "plt.ylabel(\"Fréquence d'occurrence\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f91ac0b9-d134-4d4b-bb67-a66515defee1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Lois de probabilité classiques\n",
    "## Continues\n",
    "- Fonction de densité de probabilité : $f(x)$\n",
    "- Exemples\n",
    "    - Uniforme\n",
    "    - Normale\n",
    "\n",
    "## Illustration\n",
    "Le poids d'une pomme de terre\n",
    "1. Uniforme de 120g à 240g\n",
    "2. Normale : 180g (moyenne) +- 25g (écart-type)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dceb9b8a-1e72-497b-a57b-590d926ae02f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Loi uniforme \n",
    "### Fonction de probabilité et d'échantillonnage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "af33ee8e",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "np.random.seed(12)\n",
    "b1 = 120\n",
    "b2 = 240\n",
    "\n",
    "def f(x,b1,b2):\n",
    "    if (type(x)==int) or (type(x)==float) :\n",
    "        if ((x>b1) and (x<b2)):\n",
    "            return 1/(b2-b1) \n",
    "        else:\n",
    "            return 0\n",
    "    else:\n",
    "        p = np.zeros(len(x)) \n",
    "        p[(x>b1) & (x<b2)]=1/(b2-b1)\n",
    "        return p\n",
    "        \n",
    "def weight_n_potatoes(N,b1,b2):\n",
    "    return b1+np.random.rand(N)*(b2-b1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5ebf80c1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "x1 = np.linspace(100,250,500)\n",
    "plt.plot(x1,f(x1,b1,b2),c='red')\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"pdf(x)\")\n",
    "plt.title(r'$f(x) = {:0.5f}$ '.format(1/(b2-b1)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "118be570",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 6\n",
    "x = weight_n_potatoes(N,b1,b2)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Nombre de pdt\")\n",
    "plt.hist(x,bins);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "74acb87e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 100\n",
    "x = weight_n_potatoes(N,b1,b2)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Nombre de pdt\")\n",
    "plt.hist(x,bins);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "678d04f9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 100000\n",
    "x = weight_n_potatoes(N,b1,b2)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Nombre de pdt\")\n",
    "plt.hist(x,bins);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5f96a357-b110-4b0b-a574-7f9851e0b756",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 1000000\n",
    "x = weight_n_potatoes(N,b1,b2)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Proportion de pdt\")\n",
    "plt.hist(x,bins,weights=np.ones(N)/N); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "44115755-43c9-4f11-b967-5dea4473d25f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 100000\n",
    "x = weight_n_potatoes(N,b1,b2)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Densité de pdt\")\n",
    "plt.hist(x,bins,weights=np.ones(N)/N/120*24,label=r'expérience'); # 120 grammes - 24 bins\n",
    "x1 = np.linspace(100,250,500)\n",
    "plt.plot(x1,f(x1,b1,b2),c='red',label=r'$f(x)$')\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"pdf(x)\");\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bb83c20",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exercice\n",
    "- Quel est la probabilité de trouver une pdt de 182.3 g? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "06339a27",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.008333333333333333\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "x1 = np.linspace(100,250,500)\n",
    "plt.plot(x1,f(x1,b1,b2),c='red')\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"pdf(x)\");\n",
    "print(f(182.3,b1,b2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a94c117",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "## Interprétation\n",
    "Il s'agit d'une densité de probabilité. Elle est exprimée \"par unité\". \n",
    "\n",
    "$ f(x) = 0.008333 \\neq \\mathbb  {P}(X=x) $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6cd66e9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exercice\n",
    "- Quelle est la probabilité de trouver une pdt pesant 182 -/+ 0.5 g?\n",
    "- Quelle est la probabilité de trouver une pdt pesant entre 175 et 200g?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "637ffb08",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "x1 = np.linspace(100,250,500)\n",
    "plt.plot(x1,f(x1,b1,b2),c='red')\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"pdf(x)\")\n",
    "plt.bar(np.array(range(175,200)),1/(b2-b1))\n",
    "plt.title(r'$f(x) = {:0.5f}$ '.format(1/(b2-b1)));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66c76f08",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Somme des surfaces de chaque bar : hauteur x largeur\n",
    "$(200-175) \\times 0.0083333 = 0.208$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "069cc469-1408-4936-aeef-189963a4a7cd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Fonction de répartition\n",
    "\n",
    "### Densité de probabilité\n",
    "= pdf en anglais\n",
    "$$\n",
    "f(x) = \\left\\{\n",
    "    \\begin{array}{ll}\n",
    "        0.0083333 & \\mbox{si } 120 \\leq x \\leq 240\\\\\n",
    "        0 & \\mbox{sinon.}\n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "### Fonction de répartition \n",
    "= Densité de proababilité cumulée \n",
    "= cdf en anglais\n",
    "$$F(x) = \\int_{-\\infty}^{x} f(t)dt $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30e9b62a-61e2-4b0c-9d9e-1edce7a0d556",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "$$\\int_{175}^{200} f(t)dt = F(200)-F(175) = 0.20833$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d5ceb473",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def cdf(x,b1,b2):\n",
    "    if (type(x)==int) or (type(x)==np.int64) or (type(x)==np.int32):\n",
    "        if ((x>b1) and (x<b2)):\n",
    "            return 1/(b2-b1)*(x-b1) \n",
    "        else:\n",
    "            return 0\n",
    "    else:\n",
    "        x = np.array(x)\n",
    "        p = np.zeros(len(x)) \n",
    "        zone_prop = (x>b1) & (x<=b2) \n",
    "        zone_1 = x>b2\n",
    "        p[zone_prop] = 1/(b2-b1)*(x[zone_prop]-b1) \n",
    "        p[zone_1] = np.ones(sum(zone_1))\n",
    "        return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f201afed",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "x1 = np.linspace(100,250,500)\n",
    "plt.plot(x1,cdf(x1,b1,b2),c='red')\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"pdf(x)\")\n",
    "plt.title(r'$F(x) = min(1,{:0.5f}\\times (x-{}) )$ '.format(1/(b2-b1),b1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "15e539f7",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gefvsfffZvDwAWUOQBwAAAABAQWIY0i+/mN13y5dL8fHWc+rWNU+eHTxYKlHC9jUCuCsEeQAAAAAAFASRkdKXX5oB3sGD1uOOjlKPHmaA9/DD5mEWAOwKQR4AAAAAAPbsyBFp5kxp/nwpIsJ6vFIl8+CKkSOlypVtXx+AHEOQBwAAAACAvYmPl775xuy+++mntOe0aWN233XtKjk52bI6ALmEIA8AAAAAAHtx5ow0e7YUFCRduGA9Xry4NHSoNHq0VK+ezcsDkLsI8gAAAAAAyM8MQ9q82ey++/ZbKTHRek7jxtK4cVL//lLRoravEYBNEOQBAAAAAJAfXbtmPvdu5kzp6FHrcWdn6YknzNtnH3yQwyuAQoAgDwAAAACA/CQ42AzvvvxSunnTetzb27x1dvhwqWxZm5cHIO8Q5AEAAAAAkNdiYqTly83bZ3ftsh63WKROnczuu44dJUdH29cIIM8R5AEAAAAAkFdOnpQCA6XPP5f+/tt6vHRpacQIKSBAql7d9vUByFcI8gAAAAAAsKXERGndOumzz8z/NQzrOQ8+aHbf9e4tubravkYA+RJBHgAAAAAAtnD5stl5N2uWdPq09bibmzRggDRmjOTjY/v6AOR7BHkAAAAAAOQWw5B27jSffbd8uRQXZz2ndm2z+27IEKlkSZuXCMB+EOQBAAAAAJDTIiOlr74yA7wDB6zHHR2lbt3MAK9NG/MwCwC4A4I8AAAAAABySkiINHOmNH++dOOG9XjFitKoUeZHlSq2rw+AXSPIAwAAAAAgO+LjpW+/NbvvtmxJe84jj5jdd926SU5Otq0PQIFBkAcAAAAAwN04e1aaPVsKCpLOn7ceL1bMfO7dmDHSvffavj4ABQ5BHgAAAAAAmWUYZtfdjBnSN99IiYnWcxo1MrvvBgyQPDxsXiKAgsshrwvIqi1btqhz584qW7as3NzcVLduXU2YMEFRUVF3td/Vq1f13//+V/fdd588PDzk7OysypUrq2fPntqSXks0AAAAAKBwuXZN+uQTs7POz09auTJ1iOfsbAZ3P/8s/fabFBBAiAcgx9lVkPfpp5/Kz89Pa9eulaurq+rVq6fQ0FC99dZbatq0qa5evZql/Y4fP66GDRvqnXfe0aFDh1S+fHk1aNBAkZGRWrVqldq0aaO33norl94NAAAAACDf++03yd9fqlxZeuYZ6Y8/Uo97eUnvviv99Ze0aJH0n/9wAi2AXGM3Qd6+ffs0fvx4SVJgYKDCwsIUHByskydPytfXVyEhIRo1alSW9hw9erTOnTunWrVq6eDBgzpx4oSCg4N1+fJlTZgwQZL0+uuv60BaR4UDAAAAAAqmmJh/Q7kmTczn4EVH/ztusUidOklr1kgnTkgvvyyVK5d39QIoNOwmyJs8ebKSkpI0aNAg+fv7y/LPv3BUqlRJixcvloODg1atWqWDBw9mar+IiIiUW2enTJmi+vXrp4w5OzvrzTff1H333SfDMPTDDz/k/BsCAAAAAOQvp06ZoVzVqtKgQdLOnanHS5WSXnxROn5c+v57qXNnydExb2oFUCjZRZAXGRmpdevWSZL8/f2txmvVqqU2bdpIkpYvX56pPWNjY2UYhiSpevXqac5Jfj0+Pj7LNQMAAAAA7EBi4r+hXI0a0v/+J125knrOAw9I8+dLZ85I779vzgOAPGAXQd7+/fsVGxsrFxcXNWvWLM05rVq1kiTt2rUrU3uWKVNGVatWlST9/PPPVuMxMTHau3evJOmBBx64m7IBAAAAAPnVlStmKFerlvTYY9LateaJtMnc3KQRI6S9e6Vdu6TBg83XACAPFcnrAjLj2LFjkqR77rlHTk5Oac6p8c+/iBw9ejTT+77//vvq37+/XnrpJTk4OKhLly4qXry4QkJCNGHCBIWFhalnz55q37599t8EAAAAACBvGYa0e7c0Y4a0bJkUG2s9p1YtaexYacgQydPT9jUCQAbsIshLPo22VKlS6c5JHgsPD8/0vn379lWxYsU0adIkq1t2y5Qpo+nTp2vMmDGZ2iswMFBBQUGZmhsSEpLpGgEAAAAA2RQVJS1ebAZ4+/dbjzs4SN26mQFemzbm1wCQD9lFkBcTEyPJPIQiPS4uLpKkmzdvZmnvEydO6OrVq7JYLKpatao8PT114sQJXblyRUFBQfLx8VHz5s3vuM/58+cVHBycpWsDAAAAAHLR0aPSzJnSvHnS9evW4+XLS/7+0qhR5gEXAJDP2UWQ5+rqKkmKi4tLd07sPy3Rbll4ZsG4ceM0Y8YMNW7cWAcOHFDDhg0lmYdbTJ06Va+88oratGmjn3/+WT4+PhnuVbFixTvOSRYSEpLlwBEAAAAAkAkJCdLq1Wb33aZNac956CGz+657dymDhhEAyG/sIsjz/Oe5BMm32KYlecwzk88wOHjwoGbOnKkiRYpo5cqVKc/YkyQnJye9/PLL+uOPPzR//ny99tpr+v777zPcLyAgQAEBAZm6tq+vL917AAAAAJCTzp2T5syRAgPNz29XrJh5YMWYMVL9+ravDwBygF0EebVr15YkhYWFKT4+Ps0DL06cOJFq7p3s2LFDhmGoVq1aqUK8Wz366KOaP3++9uzZc5eVAwAAAAByjWFIW7ea3Xdff212492uYUOz+27AADPMAwA7ZhdBno+Pj5ydnRUbG6s9e/aoRYsWVnO2b98uSZl6np0kRURESJIsFku6c4x/jh5PfkYfAAAAACAfuH5dWrDAfP5dWocJOjlJvXqZAV6LFlIGf+8DAHtiF0fxeHh4qEOHDpKU5smwx48f1+bNmyVJvXr1ytSeyZ17x44d08mTJ9Ocs27dOklSnTp1slwzAAAAACCHHTggBQRIlStLTz9tHeJVrSq9/bb011/SV19JLVsS4gEoUOwiyJOkCRMmyGKxaOHChQoKCkrpljt//rz69eunpKQkde/eXY0bN061rmXLlvL29tZHH32U6vUOHTqofPnySkhIUK9evfT777+njMXHx+uDDz7QvHnzJElDhgzJ1fcGAAAAAEhHbKz05ZdmZ91990lBQVJUVOo5HTpI334rnTolvfqqeRotABRAdnFrrSQ1bdpU06ZN03PPPaeAgAC99dZbKlOmjI4cOaLY2FjVqVNHs2fPtlp35swZnT59WteuXUv1uru7u7766it169ZN+/fvV8OGDXXPPffI09NTJ06cSLn19vHHH9e4ceNs8RYBAAAAAMlCQ82DKz7/XLp82Xrc01MaPlwaPVqqWdPm5QFAXrCbIE+Sxo8fr4YNG2rq1KnavXu3Ll26JC8vL/Xq1UuvvPKKPDw8srRfmzZtdPjwYX300Uf68ccfderUKZ09e1alSpVSixYtNGTIEPXt2zeX3g0AAAAAIJWkJGn9evPwirVrzcMsbte0qfnsuz59JDc329cIAHnIroI8SfLz85Ofn1+m54eGhmY47uXlpQ8//DCbVQEAAAAA7tqVK9LcudKsWVJazzB3dZX69ZPGjDGDPAAopOwuyAMAAAAAFACGIe3ZY3bfLV1qPgvvdjVrmt13Q4ZIpUrZvkYAyGcI8gAAAAAAthMdLS1ebAZ4wcHW4w4OUteuZoDn52d+DQCQRJAHAAAAALCFY8ekmTOlefOk2w4jlGSeNDtqlOTvL1WtauvqAMAuEOQBAAAAAHJHQoK0Zo3ZfbdxY9pzWrc2u+969JCcnW1bHwDYGYI8AAAAAEDOOn9emjNHCgyUzp61HvfwkAYPNg+vaNDA9vUBgJ0iyAMAAAAAZJ9hSNu2md13q1aZ3Xi3q19fGjdOGjhQKlbM9jUCgJ0jyAMAAAAA3L0bN6SFC80A78gR63EnJ6lnT/P22ZYtJYvF9jUCQAFBkAcAAAAAyLqDB83DKxYulKKirMerVpUCAqQRI6QKFWxfHwAUQJzjXcBERERo4sSJatiwoTw8PFSiRAk1bdpUU6dOVVxcXLb3v3DhgiZMmCBfX1+VKlVKbm5u8vLyUseOHfXee+8pPj4+w/V//vmnnn/+eTVo0EAlSpRQ0aJFVb16dXXv3l0zZsy44/X379+vMWPGqE6dOvLw8FDx4sVVu3Zt9e3bV4sXL7aaP3HiRFkslkx/bN269a5/bQAAAIACLzZWWrxYatVKatxYmjXLOsRr31765hvp5Enpv/8lxAOAHGQxDMPI6yIKG19fXwUHB8vHx0f79u3LsX1Pnz6thx9+WKGhoZIkd3d3JSYmKjY2VpLUpEkTbdq0SZ6enne1/9KlS+Xv768bN25IkpydneXm5qbr16+nzAkPD1fJkiXTXP/RRx/p5ZdfTqnHzc1NRYoUUUREhCSpRIkSupbWMfSSDMPQ//3f/2nq1KlKSkqSJBUtWlSGYSg6OlqS1LhxY/3222+p1k2ZMkVTpkzJ8H2Fh4crLi5OLi4uOnfunEqVKpXhfAAAAKDQOX1aCgoyD7C4dMl63NNTGjZMGj1aqlXL9vUBgB3LSk5ER14BkZiYqC5duig0NFQVK1bUjz/+qKioKEVHR2vJkiUqVqyY9u/frwEDBtzV/suXL1f//v1148YN9enTR/v371dsbKyuXbumiIgIbd++Xc8++6ycnJzSXD9t2jQ9++yziouL07hx4/THH38oOjpaN27cUHh4uDZs2KCRI0eme/1nnnlGH3zwgRwdHTVhwgSdPn1akZGRioqK0pUrV/T111+rZ8+eVuteeOEFXbhwId2PsLAwFfvnIbs9evQgxAMAAACSJSVJ69dL3bpJ1atL77xjHeL5+kpffCGdOSNNnUqIBwC5jI68PJAbHXmff/55ShD2yy+/qHnz5qnGFy9erP79+0uSNm7cKD8/v0zvff78edWvX1/h4eF69tlnNW3atCzVdujQIfn6+io+Pl4ff/yxnn766SytX7dunTp16iRJ+uabb9StW7csrc/I0qVL1bdvX0lZ/3UBAAAACqS//5bmzTOff3fihPW4q6vUt695eEXTpjYvDwAKGjryCqH58+dLkh555BGrEE+S+vbtq2rVqkmSFixYkKW9P/nkE4WHh6tKlSp67733slzbO++8o/j4eDVr1izLIZ4kTZo0SZLUu3fvHA3xJDMAlaTq1aurTZs2Obo3AAAAYFd+/dW8PbZKFemFF6xDvBo1pClTzO67uXMJ8QAgDxDkFQDR0dH6+eefJSmlc+12FotFHTt2lCRt2LAhS/snB38DBw6Us7NzltZGRUVp5cqVkqThw4dnaa0kHT9+XLt27ZIkjRgxIsvrM3L69Glt2rQppTaLxZKj+wMAAAD5XnT0v6Fcs2ZmJ15MzL/jDg5S167SunXSsWPS889LpUvnWbkAUNgR5BUAISEhKQdANGjQIN15yWMXLlzQ1atXM7X3qVOndO7cOUnSQw89pP3796tPnz6qUKGCXFxcVLVqVfXt21c7d+5Mc/2ePXtSTrJ96KGHtGXLFnXu3FllypSRq6urqlevrhEjRuj3339Pc/2OHTskSQ4ODmrZsqVWrVqlRx55RCVLlpS7u7vq1q2rZ555RmFhYZl6P7f64osvlJSUJEdHRw0dOjTL6wEAAAC7deyY9NxzZvfd8OHS3r2px8uVk1591Tx59ttvpQ4dzFAPAJCn+ElcACQHbZJUuXLldOfdOnbrmowcO3Ys5fM9e/bogQce0LJly3T9+nW5ubnpzJkzWrp0qVq0aKF333033fUWi0UrVqyQn5+f1q5dq5iYGDk5OenUqVP64osv5OPjk+Ytv8nrK1SooJdfflk9e/bUTz/9pORHOx49elSffPKJGjRokKVOw6SkJM2bN0+S2cWY0a8bAAAAUCAkJEjffCO1by/VqSN9+KEUHp56TsuW0ldfSWFh0ttvS15eeVIqACBtBHkFQERERMrn7u7u6c67dezWNRkJv+X/2CdNmqTy5ctr3bp1ioqK0rVr1xQSEiI/Pz8ZhqFXX31V33zzTbrrJ0yYoPr16+uXX35RZGSkIiIitGfPHt13332Ki4vTiBEjtPe2fwlMXn/hwgVNnz5drVu31qFDh3T9+nVFRkZq48aN8vb2VkREhHr37p3pzrwNGzakzM3pW3YBAACAfOXCBemtt6Rq1aQePaQff0w9XrSoNHq0dOCAtH271K+f5OKSN7UCADJEkIcMJd+ym/z58uXL1aFDBzn801Zft25dffvtt6pUqZIkaeLEiWmuNwxDLi4u+u6771IdxtG0aVN99913cnd3V0JCgt5666001yclJalcuXJas2ZNyi3CDg4O8vPz08qVK2WxWHTjxo1Mn6ibfMhFhQoV1Llz58z+cgAAAAD2wTCkbdvM02WrVpUmTDAPqbjVvfdK06dL586ZJ9Q2apQ3tQIAMo0grwAoVqxYyufR0dHpzrt17NY1md27ZcuWevDBB63mFC1aVGPHjpUkHThwQBcvXkxzfe/eveWVRmt+5cqV1b9/f0nSxo0blZiYmOZ6f39/FS9e3Gq9j4+P/Pz8JEnr16+/43u6cuWKVq9eLUkaMmSIihQpcsc1AAAAgF24cUOaMUNq2FB66CFp6VLzltpkRYpITzwhbd0qHT4sjRsnpfFnbABA/kSQVwAkd8NJ0tmzZ9Odd+vYrWsycuuz4+rVq5fuvFvHTp8+fdfro6Ki9Pfff9/1+luvnZ4FCxYoLi5OErfVAgAAoIA4fFgaO1aqXNkM524/TK5KFWnyZPPZd0uXSq1bSxZL3tQKALhrtCIVAPXq1ZODg4OSkpJ0+PBhderUKc15hw8flmTeTlqqVKlM7X3vvffK0dFRiYmJsmTwf/TJh09ISjWv0S3t+bZYn9GcZMm31T700EOqVavWHecDAAAA+VJcnLRqldmBt3172nPatTMDvs6dzW48AIBdoyOvAHB3d1eLFi0kSevWrUtzjmEYKbedtm/fPtN7u7q6qnXr1pKkI0eOpDsvJCREkhmkeXt7p7xes2ZNVa9ePdPrixcvrtKlS6e83qJFCxUtWjTT66tVq5bR29HOnTtT9qEbDwAAAHYpLEx67TXz2Xf9+lmHeCVLSs8+Kx09Km3YIHXvTogHAAUEQV4BMWTIEEnSli1btHv3bqvx5cuX6+TJk5KkwYMHZ2nvYcOGSZJ27NihnTt3Wo1HR0dr5syZkqQHHnhAZcuWTTU+dOjQlBpCQ0Ot1p89e1aLFy+WJD366KMpB2lIkpubm/r06SNJCgwM1I0bN6zWBwcHa/PmzZKkLl26ZPhekrvxSpYsqV69emU4FwAAAMg3kpL+DeWqVZPeflu6dCn1HB8f6fPPpbNnpWnTpNq186RUAEDuIcgrIIYMGaKGDRvKMAz17NlTmzZtkvTvSbOjRo2SJHXq1CnlYIhkEydOlMVikcViSTNoGzBggJo1ayZJ6tOnj9avX59ymuwff/yhrl276ty5c3JwcNDbb79ttf65556Tl5eXYmNj1bVrV+3atStlbO/evercubOio6Pl5uam119/3Wr9m2++qRIlSujy5cvq2rWrfv/neR+GYWjz5s3q2bOnDMNQuXLl9Nxzz6X7axQZGamlS5dKkvr37y83N7d05wIAAAD5wtWrZihXp47UoYP07bdmqJfMxUUaMkTavVvau1caPlxyd8+7egEAuYr+6gKiSJEiWr16tR555BGFhoaqbdu2cnd3V1JSkmJiYiRJTZo00ZdffpnlvR0cHPTtt9/Kz89PR44cUceOHeXm5iZnZ2ddv35dkuTk5KTPPvtMbdq0sVpftGhRrVu3Tm3bttWhQ4fUvHlzeXh4SDLDNUny8PDQ4sWL0zzQonLlylqzZo26du2qrVu3qkGDBipRooTi4+NTTuItV66c1qxZY9UNeKulS5emXG/kyJFZ/nUAAAAAbGbvXvPZd4sXS//8eT6V6tWlMWOkYcOkWx5NAwAo2OjIK0C8vb118OBBvf7662rQoIEsFoucnJzk6+urKVOmaNeuXfL09LyrvStUqKDg4GBNmTJFTZs2lbOzs27evClvb28NHz5cwcHBKV1/aalbt65+//13vf766ykHWCQmJqpOnTp6+umndfjwYXXu3Dnd9a1atdKRI0f03HPPqU6dOoqPj5ckNWzYUK+++qoOHz6c0jWYnuTban18fNSkSZOs/hIAAAAAuevmTWnePKlZM6lpU2nu3NQhnsUideki/fCDdPy49MILhHgAUMhYjFuPC4VN+Pr6Kjg4WD4+Ptq3b19elwMAAAAgL/35pzRrlvTFF1J4uPV42bLSyJGSv790y8FyAICCISs5EbfWAgAAAICtJSZKa9eat8+uX5/2nBYtpLFjpZ49zWfhAQAKPYI8AAAAALCVixfNk2UDA6WwMOvxokWlgQPN5981bmz7+gAA+RpBHgAAAABk0uWIWC39NUy7T11VZGyCPFyK6MHqpfXE/VVVtlg6XXOGIf38s9l9t2KF9M/znlOpV8/svhs0SCpRInffBADAbhHkAQAAAMAdxMQnatKa37Vi3xnFJ6Z+zPj241f00cZj6uVbVW90uVeuTo7mQESE9OWXZoB36JD1pkWKSD16mAHeQw+Zh1kAAJABgjwAAAAAyEBMfKKGfLFHu09dTXdOfKKhxXvCdPJypBY8UFQuc4KkBQvMMO92lSpJAQHmARaVKuVi5QCAgoYgDwAAAAAyMGnN7xmGeJLklBiv9sd2adBXa+Xy1+G0J/n5md13XbpITk65UCkAoKAjyAMAAACAdFyKiNGKfWfSHa9w44r6HVinfgfWq1xUuPWEEiWkoUOl0aOlunVzr1AAQKFAkIdsMQxD169fz+syAAAAgFwxb9sJxUalvj3WSEqUz8lg9Ty8SS1P/yZvSQ63rbtcs57K/t9zUr9+5km0AADkAII8ZMv169fl6emZ12UAAAAANnVG0up/Pg+V5CUp1rGIvqvbSouaPCaPh1po4cgH86w+AEDBRJAHAAAAANlwplhpfeXbRcsatlO4ewlJUpO4xDyuCgBQEBHkAQAAAEA29O33rhw9U58+6+HCX7UAADmP/3dBtpQoUULh4Wk81BcAAACwR6dOSV98IS1aJF27ZjV81bWYvqzbUq//9sO/L7oWs5r3YPXSuVgkAKCwIshDtlgsFpUsWTKvywAAAADuXmKi9P330owZ0rp1aU7ZV6muFvg8ph/qtFRMQqx0S5BnsVhSzXVytOiJ+6vmaskAgMKJIA8AAABA4XTpkvT551JgoHT6tPW4u7s0cKA+qe2naZdvOXk2ITbDbXv5VlXZYi45XCwAAAR5AAAAAAoTw5B++cXsvlu+XIqPt55Tt640dqw0eLBUooT84xP18xd7tPvU1Ttu/0C1Unqjy725UDgAAAR5AAAAAAqDyEjpyy/NAO/gQetxR0epRw8zwHv4YemW22VdnRw1f3gzTVpzRCv2/aW0+vGcHC3q5VtVb3S5V65Ojrn2NgAAhRtBHgAAAICC68gRaeZMaf58KSLCerxSJcnfXxo5UqpcOd1tXJ0c9e7jDfVcu9qa99Pveunjf8ee8quloQ/X53ZaAECuI8gDAAAAULDEx0vffGN23/30U9pz2rQxu++6dpWcnDK9ddliLhrVqrpeuuW1Ua2qqyQhHgDABgjyAAAAABQMZ85Is2ebH+fPW48XLy4NHSqNHi3Vq2fz8gAAyC6CPAAAAAD2yzCkzZvN7rtvv5USE63nNG4sjRsn9e8vFS1qPQ4AgJ0gyAMAAABgf65dM597N3OmdPSo9bizs/TEE+btsw8+mOrwCgAA7BVBHgAAAAD7ERxshndffindvGk97u1t3jo7fLhUtqzNywMAIDcR5AEAAADI32JipOXLzdtnd+2yHrdYpE6dzO67jh0lR0fb1wgAgA0Q5AEAAADIn06elAIDpc8/l/7+23q8dGlpxAgpIECqXt329QEAYGMEeQAAAADyj8REad06s/vuhx/Mwyxu9+CDZvdd796Sq6vtawQAII845HUBWbVlyxZ17txZZcuWlZubm+rWrasJEyYoKioqW/t+//33evzxx1WpUiW5uLiofPnyatGihV577TUlJCTkUPUAAAAA0nT5svS//0k1a0qdO0vff586xHNzk0aOlPbtk3bulAYNIsQDABQ6dhXkffrpp/Lz89PatWvl6uqqevXqKTQ0VG+99ZaaNm2qq1evZnnPhIQEDRo0SI899pi+/vprOTo6qnHjxvLw8NDevXv19ttvKyYmJhfeDQAAAFDIGca/oVyVKtLLL0uhoann1K4tffSRdO6cNHu25OOTF5UCAJAv2E2Qt2/fPo0fP16SFBgYqLCwMAUHB+vkyZPy9fVVSEiIRo0aleV9x4wZo0WLFqlx48bas2eP/vrrL+3Zs0cnTpxQeHi4vv32W7m4uOTwuwEAAAAKsaiof0O5//xHWrRIiov7d9zRUXr8cWnjRumPP6RnnpFKlsyzcgEAyC/s5hl5kydPVlJSkgYPHix/f/+U1ytVqqTFixerbt26WrVqlQ4ePKhGjRplas8tW7Zozpw5qlSpkjZv3qxSpUqlGnd3d1fXrl1z9H0AAAAAhdYff5jPvps/X7pxw3q8YkVp1Cjzo0oV29cHAEA+ZxcdeZGRkVq3bp0kpQrxktWqVUtt2rSRJC1fvjzT+06bNk2S9OKLL1qFeAAAAAByQHy8tGKF1KaNVK+e9Omn1iHeI49Iy5dLp09LkyYR4gEAkA676Mjbv3+/YmNj5eLiombNmqU5p1WrVtq4caN27dqVqT1jYmK0fv16SVK3bt3066+/au7cuTp+/Ljc3Nx0//33a/jw4arCHyIAAACArDt71rx9NihIOn/eerxYMWnIEGnMGOnee21fHwAAdsgugrxjx45Jku655x45OTmlOadGjRqSpKNHj2ZqzwMHDig+Pl5FixbVihUr9PLLLyspKSllfM2aNXrvvfc0f/589e7dO5vvAAAAACgEDEPassW8ffabb6TEROs5jRpJY8dKAwZIHh42LxEAAHtmF0Fe8mm0Gd3+mjwWHh6eqT3P//OvgrGxsXrppZfUsmVLffzxx2rQoIFOnz6t//73v1q+fLkGDhyo2rVrq3HjxhnuFxgYqKCgoExdOyQkJFPzAAAAALtw7Zq0YIE0c6b5HLzbOTtLvXubAV7z5pLFYvMSAQAoCOwiyIuJiZEkOTs7pzsn+WTZmzdvZmrPyMhISVJCQoLKlCmj77//XsWKFZNkPnNvyZIlOn78uH777Te9/fbbWrZsWYb7nT9/XsHBwZm6NgAAAFAg/Pab2X335ZdSdLT1uJeXNHq0NHy4VK6czcsDAKCgsYsgz9XVVZIUd+uR9LeJjY2VJLm5uWVpT8k8QCM5xEvm4OCgZ599VkOGDNH69euVlJQkB4f0zwapWLGifHx8MnXtkJCQTAeOAAAAQL4SE2MeXjFjhrRzp/W4xSJ17Gh233XqJDk62r5GAAAKKLsI8jw9PSX9e4ttWpLHkudmdk9JqlevXppzkl+/ceOGrl69qjJlyqS7X0BAgAICAjJ1bV9fX7r3AAAAYF9OnZICA6XPP5euXLEeL1VKGjFCCgiQ/nl+NQAAyFl2EeTVrl1bkhQWFqb4+Pg0D7w4ceJEqrl3Urdu3ZTPb+3Ou9Wtryem9aBeAAAAoCBLTJTWrze7777/3jzM4nYPPGB23/XuLWXy7hgAAHB3ciTIi4qK0s8//6ydO3fq3Llzunz5smJiYlS6dGmVLVtW9erV00MPPZTpkO12Pj4+cnZ2VmxsrPbs2aMWLVpYzdm+fbskqXnz5pnas3LlyvLy8tLp06dTQsDbJb/u4uKi0qVL31XtAAAAgN25ckX64gtp1iyzE+92bm5S//7SmDGSr6/t6wMAoJC66yAvPj5eK1asUFBQkH7++edUHWvGP/9SZ7ntNKry5curf//+GjVqlOrUqZPpa3l4eKhDhw5as2aNgoKCrIK848ePa/PmzZKkXr16ZXrfPn366P3339f8+fP14osvWj0D74svvpAkPfTQQypSxC6aFwEAAIC7YxjS7t1m992yZdI/z6BOpVYts/tuyBApk4+0AQAAOSf90xvScfPmTb311luqXLmyBg4cqK1btyohIUGOjo6699571bp1a/Xo0UP9+/dXhw4d1LRpU5UpU0aGYejChQv68MMPde+996pdu3bas2dPpq87YcIEWSwWLVy4UEFBQSlh4fnz59WvXz8lJSWpe/fuaty4cap1LVu2lLe3tz766COrPV944QWVKFFCISEhevbZZ1MO0zAMQx9//LHWrFkji8WiV155Jau/TAAAAIB9iIqS5swxO+uaN5cWLkwd4jk4SD16SD/+KP3xhzR+PCEeAAB5JEttZvPmzdOECRN07tw5GYahBg0aqF+/fmrdurV8fX3TfdacJIWGhmr37t369ttvtXr1am3atEmbN2/WE088offff19Vq1bN8NpNmzbVtGnT9NxzzykgIEBvvfWWypQpoyNHjig2NlZ16tTR7NmzrdadOXNGp0+f1rVr16zGypYtqxUrVqhr16765JNPtHDhQtWqVUthYWG6cOGCLBaL3n//fT388MNZ+WUCAAAA8r+jR6WZM6V586Tr163Hy5eX/P2lUaOkO/xZHQAA2EaWgrzhw4fL2dlZ/v7+Gj16tFX3W0a8vb3l7e2tPn36KDo6WitWrND777+vpUuXql69enr99dfvuMf48ePVsGFDTZ06Vbt379alS5fk5eWlXr166ZVXXpGHh0dW3o4kqW3btjpw4IDeeecdbdy4Ufv371eJEiXUtWtXPffcc3rooYeyvCcAAACQLyUkSKtXm7fPbtqU9pyHHjJvn+3eXXJ2tml5AAAgY1kK8gICAvTqq6/esXvuTtzd3TV48GANGjRIy5cvV3x8fKbX+vn5yc/PL9PzQ0ND7zinVq1amjt3bqb3BAAAAOzKuXPm7bNBQdLZs9bjxYpJgwebh1fUr2/7+gAAQKZkKcibOXNmjl7cYrHoiSeeyNE9AQAAAMg8vGLrVrP77uuvzW682zVsaHbfDRhghnkAACBf4yhWAAAAoCC5ft08sGLGDCkkxHrcyUnq1csM8Fq0kCwW29cIAADuSp4EeVeuXFGZMmXy4tIAAABAwXTggHl4xaJF5km0t6taVRo9WhoxwjzIAgAA2B2H7G7QqVMnXb58OdPzf/zxRzVq1Ci7lwUAAAAQGyt99ZXUsqV0331SYKB1iNehg/Ttt9KpU9KrrxLiAQBgx7Id5K1fv16NGzfWhg0bMpyXkJCgl156SZ06ddLFixeze1kAAACg8AoNlV55xeyyGzBA+vnn1OOentLzz0vHj0vr1kldu0qOjnlSKgAAyDnZvrW2evXqOnnypB599FE9++yzevfdd1WkSOptT5w4oX79+mnfvn0yDEN9+/bN7mUBAACAwiUpSVq/3nz23dq15mEWt2va1Hz2XZ8+kpub7WsEAAC5Ktsdeb/99psGDBigpKQkTZs2Tc2bN9eJEydSxhcsWCAfHx/t3btX7u7u+vzzz/XVV19l97IAAABA4fD339IHH0i1akmPPip9913qEM/VVRo2TNqzx/wYOpQQDwCAAirbHXkeHh5auHCh2rVrpyeffFL79u1TkyZNNGXKFG3btk2LFy+WYRhq0qSJFi9erNq1a+dE3QAAAEDBZRhmKDdjhrR0qfksvNvVrGl23w0ZIpUqZfsaAQCAzeXYqbWDBw/Wf/7zH/Xv31979+7VmDFjUsbGjx+v//3vf3JycsqpywEAAAAFT3S0tHixGeAFB1uPOziYz7sbO1by8zO/BgAAhUaOBXmSVLNmTXXu3Fl79+6VYRiyWCxq2LChXn31VUI8AAAAID3HjkkzZ0rz5knXrlmPly8vjRol+fubB1wAAIBCKcf+Ce/ixYtq166dJk2aJEm6//77VaRIER06dEiNGzfWxo0bc+pSAAAAgP1LSJC+/lpq106qU0f66CPrEK91a2nJEiksTJo8mRAPAIBCLkeCvB9++EGNGjXS5s2b5eTkpClTpmjPnj3avn27vL29df78eXXs2FEvvfSSEhIScuKSSEdERIQmTpyohg0bysPDQyVKlFDTpk01depUxcXF5ei1Ro8eLYvFIovFIm9v73TnDR06NGVeRh8Z/d64efOmPvzwQ7Vq1UqlS5eWk5OTSpQoIV9fX/33v//VhQsX0lwXHx+v2bNnKyAgQA888ICqVq0qNzc3ubu7q0aNGurfvz8hMwAAsK3z581Qzttbevxx6fY/i3h4mLfOHjokbd1qnkDr7JwnpQIAgPzFYhhpnVufec8995w+/vhjGYahmjVrasmSJfLx8UkZj4iI0OjRo7V48WJZLBb5+Pho8eLFqlmzZraLt1e+vr4KDg6Wj4+P9u3bl2P7nj59Wg8//LBCQ0MlSe7u7kpMTFTsPw9HbtKkiTZt2iRPT89sX+unn35SmzZtlPzbx8vLK+W6txs6dKjmz58vV1dXlShRIt09z549K0dHR6vXT58+rXbt2un48eMpr5UoUUIRERFKSkpK+Xr16tVq3bp1qrVXrlxR2bJlU762WCwqWbKkbty4ocTExJTXhwwZojlz5qhIkRy92xwAAMBkGNK2beaz71atMrvxble/vjRunDRwoFSsmO1rRKZdu3Yt1Z+pw8PDVbJkybwrCABg17KSE2W7I++jjz6SYRgaNGiQ9u/fnyrEk6RixYrpyy+/1Ny5c1W0aFHt27fPag6yLzExUV26dFFoaKgqVqyoH3/8UVFRUYqOjtaSJUtUrFgx7d+/XwMGDMj2taKjozVy5EgVKVJE999/f6bX9enTRxcuXEj3I60QTzIPUjl+/LicnZ01ffp0RURE6Nq1a7p586a+/fZbVa5cWdevX9cTTzyhmzdvplrr4uKip556SkuXLlVoaKhiY2N19epVxcXF6dChQ+rbt68kaf78+ZoyZcrd/6IAAACk5cYN6bPPpAYNpIcflpYtSx3iOTlJffuaId+hQ9KYMYR4AAAgXdkO8ooVK6ZFixZp/vz5Klq0aLrzhgwZouDgYPn6+ioqKiq7l8Vt5s2bp0OHDkmSVq5cqbZt20qSHBwc1KdPHwUGBkoyb4PetGlTtq713//+VydOnNBLL72k+vXrZ6/wOzh9+rS2bdsmSXrllVc0btw4eXh4SJKcnZ3VtWtXzZ8/X5L5nMbkucmKFSumTz75RE888YS8vLxSDl1xcHBQgwYN9NVXX+k///mPJOnzzz/P1fcCAAAKkeRQrlIl6cknpSNHUo9XrSq99Zb57LvFi6VWrSSLJW9qBQAAdiPbQV5wcLD69++fqbk1a9bUzp079fzzz2f3srhNcpj1yCOPqHnz5lbjffv2VbVq1SRJCxYsuOvr7Nq1S5988olq166t11577a73yazz58+nfJ5e91+zZs1SPo+MjMzS/haLRQ888IAk6cyZM3dRIQAAwD9iY/8N5Ro1kmbNkm7/B+z27aVvvpFOnpT++1+pQoU8KRUAANinbAd5NWrUyNL8IkWK6P3338/uZXGL6Oho/fzzz5KkTp06pTnHYrGoY8eOkqQNGzbc1XViY2M1fPhwGYahwMBAubq63l3BWVC9evWUz/fu3ZvmnD179kgyu+yaNGmSpf2TkpL0yy+/SMr672UAAABJZlfdf/8r3XOP1L+/tGNH6nFPT+m556Rjx6T166Vu3SSeywsAAO5Cjpxai7wVEhKScuhDgwYN0p2XPHbhwgVdvXo1y9d58803FRISohEjRujhhx/O8vpNmzapdu3acnV1VfHixdWwYUONHz8+1SEWtytXrpwef/xxSdK7776rzz77LKXrLj4+XqtXr9aQIUMkSc8//3yq4C8jV69e1Y4dO9SjRw/t3r07ZT0AAECmJCX9G8pVqya984506VLqOb6+0hdfSGfOSFOnSrVq5U2tAACgwMhSkHf27NlcKeLW2yeRdefOnUv5vHLlyunOu3Xs1jWZsX//fr3//vsqX778XXdUnjlzRidPnpS7u7uio6N1+PBhffzxx2rQoIFmzpyZ7ro5c+aoQ4cOiouL05NPPqlixYqpZMmScnV1Vbdu3VSqVCnNnj37jnW99957slgsslgsKl26tFq1aqXVq1fLw8NDH374oYYNG3ZX7wsAABQif/9thnK1a0sdO0qrV5uhXjJXV2noUGnPHmnvXmnYMMndPc/KBQAABUuWgryaNWvq6aefznIIlJ4VK1aoUaNGmj17do7sV1hFRESkfO6ewR8Ubx27dc2dJCQkaPjw4UpISNAnn3wiT0/PLNXn4+Oj6dOnpzo19saNG1q5cqVq1KihuLg4jR07VitWrEhzvaenp1atWqXnn39eln8eAn39+vWULsTIyEhduXJFiYmJGdbh4eGh8uXLq2zZsin7uLu7a/LkyRoxYkSW3hMAAChkfv3VDOWqVJFeeEE6cSL1eI0a0pQpZvfd3LlS06Z5UycAACjQshTkVapUSdOnT1fNmjXVt29frVmzRgkJCVm64IkTJ/Tmm2+qdu3a6tOnj44cOSJvb+8s7QHbeu+99/Tbb7+pc+fOeuKJJ7K8/umnn9a4cePk5eUlR0dHSWaA9vjjj2v37t0p//1feOEFGYZhtX7//v2qW7euPvzwQ40dO1aHDh1SVFSUTpw4oY8++khXr17VK6+8oi5duqSEe2l58skndeHCBV26dEk3b97Uzp071bJlSz377LPy9fXV0aNHs/zeAABAARYd/W8o16yZNG+eFBPz77iDg9S1q7Runfn8u+efl0qXzrNyAQBAwZelp+z+8ccf+uSTT/T2229r2bJlWr58uUqWLKkHHnhAzZo1U+PGjVW2bFmVKlVKLi4uCg8P19WrV3Xy5Ent2bNHu3fv1h9//CFJMgxD7du315QpUzJ8rhvurFixYimfR0dHpzvv1rFb12TkyJEjmjx5sjw8PDRjxoy7LzIdpUuX1n//+1+NGjVKp0+f1v79++Xj45MyHhERoU6dOunixYt6/fXXNWnSpJSx6tWr65lnnlGDBg3Url07/fDDD5o7d26muutcXFz04IMPat26derevbtWr16tgQMHas+ePSndegAAoJA6ftw8cXbuXCk83Hq8XDlp5EjJ31/y8rJ9fQAAoNDKUpDn5OSk559/XsOHD1dgYKDmzJmjkydPat26dVq/fv0d1xuGIWdnZ3Xv3l3jxo1Tq1at7rpw/KtSpUopn589e1aNGjVKc96tzzi8dU1Gxo0bp7i4OE2aNEmenp4pB00kS+7INAwjZczFxUVOTk6Zrr958+Ypn588eTJVkLdo0SJdvHhRUvqHUfj5+alJkyYKDg7WypUrs3SbrMVi0fjx47V69Wrt3bvXKkgEAACFREKCtHatNGOGtGFD2nNatpTGjpUef1xycbFtfQAAALrLU2s9PT318ssv688//9SGDRv03HPPydfXVw4ODjIMw+qjfPny6t27t2bMmKG//vpLS5YsIcTLQfXq1ZODg/mf8vDhw+nOSx6rUKGCSpUqlam9T506JUl65ZVXVKxYMauPL7/8UpIUFhaW8tpnn32WnbeTypEjRyRJZcuWVfHixdOdV+ufU+CS682KWw8B+fPPP7O8HgAA2LELF6S335aqV5e6d7cO8YoWlUaPlg4ckLZvl/r1I8QDAAB5JksdeWlp27at2rZtK0mKj4/XpUuXdPnyZcXExKh06dIqW7asSpYsmd3LIAPu7u5q0aKFtm/frnXr1unFF1+0mmMYRkrXZPv27W1dYoZ27dqV8nm1atVSjSUHlFeuXFFUVJSKFi2a5h7JXXuZvWX4VidPnkz5/G7WAwAAO2MY0o4dZvfdypVSfLz1nHvvNbvvBg2SMvjHRAAAAFvKUkfejRs3rG6tvJWTk5MqV66s++67Tw8++KBq1apFiGcjQ4YMkSRt2bJFu3fvthpfvnx5SmA1ePDgTO8bGhqaZpdl8kfydb28vFJeGz9+fMr6tA6vuNXVq1f1zjvvSJKqVKmiJk2apBpPvs3VMAwFBgamucfhw4e1Y8cOSalv05V0x8NYEhIS9MEHH0iSnJ2drdYDAIAC5MYNM7xr1Ehq3VpasiR1iFekiPTEE9LWrdLhw9K4cYR4AAAgX8lSkFeyZEnVqVMn1Wtvvvmmpk2blqNFIeuGDBmihg0byjAM9ezZU5s2bZIkJSUlafny5Ro1apQkqVOnTvLz80u1duLEibJYLLJYLAoNDc3RuhYtWqTHH39cK1eu1KVLl1Jev3nzpr755hs9+OCDKQHjlClTUjrwkvXq1UsVK1aUJL366qt6++239ffff0uSoqKitGTJErVv314JCQlydnbWk08+mWr9U089pTFjxuinn35KFULHxsZq8+bNatu2rTZv3izJPDWX4BkAgALo8GGzu65yZTOcu/1RJFWqSJMnS2Fh0tKlZsjH4VcAACAfyvKttbd3WE2cOFEVKlTQc889l2NFIeuKFCmi1atX65FHHlFoaKjatm0rd3d3JSUlKSYmRpLUpEmTlGfa2UpiYqK+/vprff3115KkokWLytXVVdeuXVNiYqIk83CMadOmqU+fPlbrixYtqm+++UadO3fW5cuX9dprr+m1115TsWLFFBkZmfL70d3dXfPnz095Vl6ymzdvav78+Zo1a5YsFouKFSsmJyenVNe3WCx6+umnNXny5Nz8pQAAALYUFyetWmV24G3fnvacdu3MgK9zZ7MbDwAAIJ/L0p9YnJ2dFRUVlVu1IJu8vb118OBBTZkyRatWrdKpU6fk5OSk+vXrq1+/fnrqqafk7Oxs05oeeeQRvf3229q5c6dCQkL0999/6/r16ypevLhq1qypNm3aKCAgwOrZeLdq1qyZQkJCNHPmTK1du1ZHjx7VjRs3VLRoUVWvXl1+fn568sknVb16dau1L7/8surXr6+tW7fq2LFjunTpUsr1q1evrpYtW2rYsGFq3Lhxbv4yAAAAWwkLk4KCpDlzpH+eoZtKyZLSsGHmARa1a9u8PAAAgOywGHd6iNktatasqVOnTmnHjh0pzxJzcHBQhQoVdO7cuVwrsqDx9fVVcHCwfHx8tG/fvrwuBwAAwL4lJUkbN5rdd2vWmF/fzsfHvK22b1/J3d32NaJAuXbtmjw9PVO+Dg8P5xEtAIC7lpWcKEsdeY8++qimT5+uRx55RI0aNZKHh4ck88CCNm3aZHofi8WS8gw3AAAA4K5cvSrNmyfNnCn9+af1uIuLGdyNHSs1bcpz7wAAgN3LUpA3adIkbd++XQcOHNDevXtTXo+Li9NPP/2U6X0s/CEKAAAAd2vvXrP7bvFi6Z9nAadSvbo0Zox5C23p0ravDwAAIJdkKcjz9PTUvn379OOPP+rQoUOKjo7WxIkT5eHhoeeffz63agQAAEABcjkiVkt/DdPuU1cVGZsgD5cierB6aT1xf1WVLeaS9qKbN80TZWfMkH791XrcYjEPrRg7VmrfXnJwyN03AQAAkAeyfDyXg4ODOnTooA4dOkhSSpD3xhtv5HhxAAAAKDhi4hM1ac3vWrHvjOITUz+mefvxK/po4zH18q2qN7rcK1cnR3Pgzz+lWbOkL76QwsOtNy1bVho5UvL3l7y9c/9NAAAA5KEsB3m3Gzx4MA92BQAAQIZi4hM15Is92n3qarpz4hMNLd4TplMXr2tB+StyDpolrV+f9uQWLczuu549zWfhAQAAFALZDvLmzZuXA2UAAACgIJu05vcMQzxJKhMVricO/qj+M3+Q843L1hOKFpUGDjSff9e4cS5VCgAAkH9lO8gDAAAAMnIpIkYr9p1Je9AwdP/ZIxoU/L06Hf1ZzkkJ1nPq1TO77wYNkkqUyN1iAQAA8rEsBXlvvvlmjl349ddfz7G9kHcMw9D169fzugwAAJCPzdt2QrFREalec4uJVtvfN6vH71tUK/ysqkq69XiKeAdHnW7VXjUnviQ99JB5mAUAAEAhl6Ugb+LEibJk8w9RhmHIYrEQ5BUQ169fl6enZ16XAQAA7NAxSTP++TxUkpekCx6l9NV9nbSkUXvV8amjhQ8/kGf1AQAA5DdZCvJat26dbpD322+/pXRmVa5cWVWqVJEknT17VmfOmLdSlCxZUo15ngkAAABus6dyPb3TtIc21WymBEfzj6iVY9O4zRYAAKAQy1KQ99NPP6X5+iuvvKKtW7eqX79+mjhxomrVqpVq/M8//9SkSZP05Zdfqnnz5nrnnXfuumAAAAAUPM92eUFFSpRP9ZqHC49zBgAAuFW2/3S0cuVKvf/++xo7dqymT5+e5pyaNWtq4cKFKlGihP73v//p/vvv1+OPP57dSyMfKFGihMLDw/O6DAAAkF8kJUnbtklz5kg//GB+fZuQMl6af+/DCtw2P+U1i7O71bwHq5fO1VIBAADsTbaDvOnTp8tisWjixIl3nDtx4kTNnDlT06dPJ8grICwWi0qWLJnXZQAAgLwWHi7Nny/NnCkdO2Y1HOdYRGvqttKiJo9pf6U6SoqNkm4N8m57fIuTo0VP3F8118sGAACwJ9kO8g4ePKgSJUqoTJkyd5xbpkwZlSxZUgcOHMjuZQEAAJAfBAdLM2ZIX30l3bxpPV6tmjR6tP5X7gF9/kdkprft5VtVZYu55GChAAAA9i/bQV5sbKxiY2MVGRkpDw+PDOdGRkbqxo0bcnHhD2UAAAB2KyZGWrbMDPB277Yet1ikxx6TxoyROnSQHB31YnyiDn+xR7tPXb3j9g9UK6U3utybC4UDAADYN4fsblCnTh0lJSWl+3y8W02fPl2JiYmqU6dOdi8LAAAAWztxQnrpJalyZWnIEOsQr0wZ6eWXzXlr1kiPPio5OkqSXJ0cNX94M/Vrdo+cHC1pbG7eTtuv2T2aP7yZXJ0cc/vdAAAA2J1sd+QNGzZMTz/9tF577TXFxsbq+eeft+rMi4qK0tSpU/Xmm2/KYrFo2LBh2b0sAAAAbCExUfr+e7P7bv16yTCs5zRvLo0bJ/XqJWVw54Wrk6PefbyhnmtXW/N++l0vffzv2FN+tTT04frcTgsAAJABi2Gk9aexzEtKStKjjz6qDRs2yGKxyM3NTffff78qV64si8WiM2fOaO/evbp586YMw1C7du30ww8/yMEh282AdsvX11fBwcHy8fHRvn378rocAAAAa5cuSZ9/LgUGSqdPW4+7u0sDB5q3z953X5a3v3btmjw9PVO+Dg8P5wAt2A1+/wIAclJWcqJsd+Q5ODho9erVevnllzV9+nRFR0dr27ZtKSePJeeERYoU0dixY/W///2vUId4AAAA+ZZhSL/8YnbfLV8uxcdbz6lbVxo7Vho8WCpRwvY1AgAAFGLZDvIkydnZWdOmTdOLL76oFStWaO/evbp06ZIkqVy5crr//vvVs2dPVapUKScuBwAAgJwUGSl9+aUZ4B08aD3u6Cj16GEGeA8/bB5mAQAAAJvLkSAvWcWKFfXUU0/l5JYAAADILUeOSDNnSvPnSxER1uOVKkn+/tLIkeYBFwAAAMhTORrkSdLvv/+eZkde/fr1c/pSAAAAyKr4eOmbb8zuu59+SntOmzZm913XrpKTky2rAwAAQAZyLMj77rvv9Morr+jIkSNpjt977716++231bVr12xdZ8uWLZo6dap2796tyMhIeXl5qXfv3nr55ZdVtGjRbO0tSd9//70ee+wxSZKXl5dCQ0OzvScAAECeO3NGmj3b/Dh/3nq8eHFp6FBp9GipXj2blwcAAIA7y5FTJ958801169ZNv//+uwzDkKOjo8qVK6dy5crJ0dFRhmHo999/V48ePTRx4sS7vs6nn34qPz8/rV27Vq6urqpXr55CQ0P11ltvqWnTprp69Wq23kdERIRGjx6drT0AAADyDcOQNm2SevaUvL2lN9+0DvEaN5aCgqRz56SPPybEAwAAyMeyHeStW7dOEydOlGEYat26tTZs2KDIyEidP39e58+fV2RkpDZs2KCHH35YhmFo8uTJWr9+fZavs2/fPo0fP16SFBgYqLCwMAUHB+vkyZPy9fVVSEiIRo0ala338n//93/666+/1L1792ztAwAAkKeuXfs3lGvbVlq1SkpM/Hfc2VkaONA8oXb/fmnUKCkH7mwAAABA7sp2kDdt2jRJUu/evbVlyxa1bdtWzs7OKePOzs5q27atNm3apN69e8swjJQ1WTF58mQlJSVp0KBB8vf3l+Wf09IqVaqkxYsXy8HBQatWrdLBtE5ay4QdO3Zo1qxZ6tGjh7p163ZXewAAAOSp5FCuUiVp/Hjp6NHU497e0nvvmbfZLlwoNW/OCbQAAAB2JNtB3t69e2WxWDRt2rSUcC0tFotFU6dOlST9+uuvWbpGZGSk1q1bJ0ny9/e3Gq9Vq5batGkjSVq+fHmW9pakmJgYjRw5Uh4eHvr000+zvB4AACDPxMT8G8r5+Ehz5kg3b/47brFIjz4qffed9Oef0v/9n1S2bN7VCwAAgLuW7cMu4uLiVLJkSVWuXPmOc6tUqSJPT0/FxcVl6Rr79+9XbGysXFxc1KxZszTntGrVShs3btSuXbuytLdkPuPv6NGj+vTTTzP1PgAAAPLcyZNSYKD0+efS339bj5cuLY0YIQUESNWr274+AAAA5LhsB3nVq1fX0aNHFRcXl+qW2rTExsYqMjJSdevWzdI1jh07Jkm655575OTklOacGjVqSJKO3n4LyR389ttv+uCDD9SsWTONHTs2S2sBAABsKjFRWrdOmjFD+uEH8zCL2z34oDR2rNS7t+TqavsaAQAAkGuyHeT1799fr776qhYsWKCRI0dmOHfhwoWKj49X//79s3SN5NNoS5Uqle6c5LHw8PBM75uYmKgRI0ZIkoKCguTgcPd3GgcGBiooKChTc0NCQu76OgAAoBC6fFn64gtp1iwpNNR63M1NGjBAGjPGvL0WAAAABVK2g7znn39e33//vZ5++mk5OTlpyJAhac5bsGCBnn76abVq1UrPP/98lq4RExMjSRl2/Lm4uEiSbt76TJg7mDJlioKDg/XSSy+pcePGWarpdufPn1dwcHC29gAAAEhhGNKuXWb33bJlUlqPJqld2+y+GzJEKlnS5iUCAADAtrId5L377rtq3bq1Dh06pOHDh+uNN97Qww8/rMqVK8tisejMmTPaunWrwsLCVKJECbVq1UrvvPNOmnu9/vrrab7u+s9tIRk9Wy82NlaS5Obmlqm6jx8/rokTJ6patWp64403MrUmIxUrVpRPJv8FPCQkJEuBIwAAKESioqSvvjIDvN9+sx53dJS6dTMDvDZtOHUWAACgEMl2kDdx4sSU02oNw1BYWJgWLlyYao7xz/Nbrl+/rnfffTfdvdIL8jw9PSX9e4ttWpLHkufeyejRoxUTE6OZM2fK3d09U2syEhAQoICAgEzN9fX1pXsPAACk9scf0syZ0rx50o0b1uMVK0qjRpkfVarYvDwAAADkvWwHea1bt04J8nJL7dq1JUlhYWGKj49P88CLEydOpJp7J/v27ZPFYknzVuDkbrm//vpLFSpUkCStWrVK//nPf+6qfgAAgDTFx0urV5vdd5s3pz3nkUfM7rtu3aR0Dv0CAABA4ZDtIO+nn37KgTIy5uPjI2dnZ8XGxmrPnj1q0aKF1Zzt27dLkpo3b57pfQ3D0MWLF9MdT0pKShnP6LZeAACALDl3Tpo9WwoKMj+/XbFi5nPvxoyR7r3X9vUBAAAgX7r7Y1ptyMPDQx06dJCkNE+GPX78uDb/86/YvXr1ytSe165dk2EYaX7MnTtXkuTl5ZXy2sMPP5wzbwYAABROhiFt2SL17i3dc480caJ1iNeokXky7blz0qefEuIBAAAgFbsI8iRpwoQJslgsWrhwoYKCglKeu3f+/Hn169dPSUlJ6t69u9Xpsy1btpS3t7c++uijPKgaAAAUetev/xvKtWkjrVghJSb+O+7sLA0YIP38s3m4RUCA5OGRZ+UCAAAg/7KbIK9p06aaNm2aJPNgCS8vL/n4+KhatWrat2+f6tSpo9mzZ1utO3PmjE6fPq1r167ZuGIAAFCo/fab5O8vVaokPf20eZjFrby8pHfflf76S1q0SPrPfziBFgAAABnK9jPybGn8+PFq2LChpk6dqt27d+vSpUvy8vJSr1699Morr8iDf70GAAB5KSbG7LibMUPaudN63GKROnY0D6/o1ElydLR9jQAAALBbdhXkSZKfn5/8/PwyPT80NDTL1xg6dKiGDh2a5XUAAKCQOnVKCgyUPv9cunLFerxUKWnECPO22Ro1bF8fAAAACgS7C/IAAADyhcREaf16s/vu++/Nwyxu98ADZvdd796Sm5vtawQAAECBQpAHAACQFVeuSF98YZ4ue+qU9bibm9S/vzRmjOTra/v6AAAAUGAR5AEAANyJYUi7d5vdd8uWSbGx1nNq1TK774YMkTw9bV8jAAAACjyCPAAAgPRERUmLF5sB3v791uMODlK3bmaA16aN+TUAAACQSwjyAAAAbnf0qDRzpjRvnnT9uvV4+fKSv780apRUtarNywMAAEDhRJAHAAAgSQkJ0urVZvfdpk1pz3noIbP7rnt3ydnZpuUBAAAABHkAAKBwO39emj1bCgqSzp61Hi9WTBo82Dy8on5929cHAAAA/IMgDwAAFD6GIW3danbfff212Y13u4YNze67AQPMMA8AAADIYwR5AACg8Lh+XVq40AzwQkKsx52cpF69zACvRQvJYrF9jQAAAEA6CPIAAEDBd+CAeXjFokXmSbS3q1pVGj1aGjHCPMgCAAAAyIcI8gAAQMEUGyutXGl23/38c9pzOnQwu+8ee0xydLRtfQAAAEAWEeQBAICC5fRpKTBQmjNHunzZetzTUxo+3OzAq1nT9vUBAAAAd4kgDwAA2L+kJGnDBrP77rvvzMMsbte0qdl916eP5OZm+xoBAACAbCLIAwAA9uvvv6W5c83n3508aT3u6ir16yeNGWMGeQAAAIAdI8gDAAD2xTCkX381u++WLDGfhXe7mjXN7rshQ6RSpWxfIwAAAJALCPIAAIB9iI6WFi82u+/27bMed3CQunY1Azw/P/NrAAAAoAAhyAMAAPnbsWNmeDdvnnTtmvV4+fLSqFGSv79UtaqtqwMAAABshiAPAADkPwkJ5qEVn30mbdyY9pzWrc3uux49JGdn29YHAAAA5AGCPAAAkH+cPy/NmSMFBUlnzliPe3hIgwebh1c0aGD7+gAAAIA8RJAHAADylmFI27aZh1esWmV2492ufn1p3Dhp4ECpWDHb1wgAAADkAwR5AAAgb9y4IS1caAZ4R45YjxcpIvXqZd4+27KlZLHYvkYAAAAgHyHIAwAAtnXokBneLVokRUZaj1etKgUESCNGSBUq2L4+AAAAIJ8iyAMAALkvLk5audIM8HbsSHtO+/Zm991jj5ndeAAAAABS4U/JAAAg94SFSYGB5gEWly5Zj3t6SsOGSaNHS7Vq2b4+AAAAwI4Q5AEAgJyVlCT9+KPZfffdd+bXt/P1NQ+v6NNHcne3fY0AAACAHSLIAwAAOePqVWnuXGnmTOnECetxV1epb1/z9tmmTW1fHwAAAGDnCPIAAED2/Pqr2X23ZIkUE2M9XqOGNGaMNHSoVLq0zcsDAAAACgqCPAAAkHXR0dLSpWaAt3ev9biDg9S5s9l9166d+TUAAACAbCHIAwAAmXf8uDRrlnkLbXi49Xi5ctLIkZK/v+TlZfv6AAAAgAKMIA8AAGQsIUFau9bsvtuwIe05LVua3XePPy65uNi2PgAAAKCQIMgDAABpu3hRmjNHCgyU/vrLerxoUWnQIPP5d40a2b4+AAAAoJAhyAMAAP8yDGnHDrP7buVKKT7ees6995rdd4MGScWL275GAAAAoJAiyAMAAFJEhLRokRngHT5sPV6kiHnb7LhxUqtWksVi+xoBAACAQo4gDwCAwuzwYWnmTGnBAiky0nq8ShUpIEAaMUKqWNH29QEAAABIQZAHAEBhExcnff212X23bVvac9q1M2+f7dzZ7MYDAAAAkOf4kzkAAIXFX39JQUHS7NnmQRa3K1lSGjZMGj1aql3b5uUBAAAAyBhBHgAABVlSkrRxo9l9t2aN+fXtfHzMZ9/17Su5u9u+RgAAAACZQpAHAEBBdPWqNG+e+fy7P/+0HndxMYO7sWOlpk05vAIAAACwAwR5AAAUJPv2SZ99Ji1eLMXEWI9Xry6NGWPeQlu6tO3rAwAAAHDXCPIAALB3N29KS5eat8/++qv1uMViHloxdqzUvr3k4GD7GgEAAABkG0EeAAD26s8/pVmzpC++kMLDrcfLlpVGjpT8/SVvb5uXBwAAACBnEeQBAGBPEhOltWvN7rv169Oe06KF2X3Xs6f5LDwAAAAABQJBHgAA9uDiRenzz6XAQCkszHq8aFFp4EDz+XeNG9u+PgAAAAC5jiAPAID8yjCkn382u+9WrJDi463n1Ktndt8NGiSVKGH7GgEAAADYDEEeAAD5TUSE9OWXZoB36JD1eJEiUo8eZoD30EPmYRYAAAAACjyCPAAA8ovff5dmzpQWLDDDvNtVqiQFBJgHWFSqZPv6AAAAAOQpgjwAAPJSXJz0zTdm993WrWnP8fMzu++6dJGcnGxaHgAAAID8gyAPAIC8cOaMFBQkzZ4tXbhgPV6ihDR0qDR6tFS3rs3LAwAAAJD/EOQBAGArSUnS5s1m993q1VJiovWc++6Txo2T+vUzT6IFAAAAgH8Q5AEAkNvCw6X5883n3x07Zj3u7Cz16WPePvvAAxxeAQAAACBNBHkAAOSW4GCz++6rr6SbN63Hq1Uzb50dPlwqU8b29QEAAACwKwR5AADkpJgYadkyM8Dbvdt63GKRHntMGjNG6tBBcnS0fY0AAAAA7JJDXheQVVu2bFHnzp1VtmxZubm5qW7dupowYYKioqKytI9hGPrll1/08ssvq2XLlipdurScnJxUtmxZtW/fXl9++aUMw8ildwEAKHBOnJBeekmqUkUaMsQ6xCtTRnr5ZXPemjXSo48S4gEAAADIErvqyPv000/1zDPPyDAMValSRVWrVtWRI0f01ltvaeXKldqxY4dKlSqVqb02b96stm3bpnxdvXp1VatWTadOndKPP/6oH3/8UYsXL9bKlSvl4uKSW28JAGDPEhOlH34wu+/WrZPS+geg5s3Nwyt69ZL4/xMAAAAA2WA3HXn79u3T+PHjJUmBgYEKCwtTcHCwTp48KV9fX4WEhGjUqFGZ3s8wDFWrVk0ff/yxLl68qBMnTmjv3r36+++/tWDBArm4uGjt2rV64403cukdAQDs1qVL0nvvSTVqSF26mGHerSGeu7vk7y/t3y/98os0YAAhHgAAAIBss5sgb/LkyUpKStKgQYPk7+8vyz8n+lWqVEmLFy+Wg4ODVq1apYMHD2Zqv2bNmuno0aN6+umnVa5cuVRjgwYN0uuvvy5Jmj17tpKSknL2zQAA7I9hmKHcwIFS1arSK69Ip0+nnlO3rvTJJ9K5c1JgoHTffXlSKgAAAICCyS6CvMjISK1bt06S5O/vbzVeq1YttWnTRpK0fPnyTO1ZvHhxOTk5pTveqVMnSdLVq1d1+fLlrJYMACgoIiOloCCpSROpRQvpyy+luLh/xx0dzdtmN2+WjhyRnnpKKlEi7+oFAAAAUGDZxTPy9u/fr9jYWLm4uKhZs2ZpzmnVqpU2btyoXbt25cg1Y2JiUj53c3PLkT0BAHbkyBFp5kxpwQLpxg3r8UqVzNtnR46UKle2fX0AAAAACh27CPKOHTsmSbrnnnvS7aKrUaOGJOno0aM5cs3FixdLkho3bqzixYvnyJ4AgHwuPl765hvz8Iqffkp7Tps20tixUteuUgad3QAAAACQ0+wiyLt69aokZXgibfJYeHh4tq8XHBysWbNmSZJefvnlTK0JDAxUUFBQpuaGhITcdW0AgFxw9qx5++zs2dL589bjxYtLQ4dKo0dL9erZvDwAAAAAkOwkyEu+zdXZ2TndOS7/nAZ48+bNbF3r4sWL6tGjh+Lj49WjRw/17ds3U+vOnz+v4ODgbF0bAGBDhmE+127GDOnbb6XEROs5jRtL48ZJ/ftLRYvavkYAAAAAuIVdBHmurq6SpLhbHy5+m9jYWEnZe57d9evX1alTJ4WFhcnX11fz5s3L9NqKFSvKx8cnU3NDQkKyHTgCAO7StWvS/Pnm8+/SehyDs7P0xBPm7bMPPij9c0o6AAAAAOQ1uwjyPD09Jf17i21akseS52ZVZGSkOnbsqP3796t+/fpav359lp6NFxAQoICAgEzN9fX1pXsPAGxt/36z++6rr6ToaOtxb2/z1tnhw6WyZW1eHgAAAADciV0EebVr15YkhYWFKT4+Ps0DL06cOJFqblZER0frscce065du1S7dm1t3LhRpUuXzl7RAIC8FxMjLV9uBnhpnWpusUidOpnddx07So6Otq8RAAAAADLJLoI8Hx8fOTs7KzY2Vnv27FGLFi2s5mzfvl2S1Lx58yztHRMTo27dumnbtm3y9vbWpk2bVKFChRypGwCQR06dkmbNkj7/XPr7b+vx0qWlESOkgACpenXb1wcAAAAAd8EhrwvIDA8PD3Xo0EGS0jwZ9vjx49q8ebMkqVevXpneNz4+Xj179tTGjRtVpUoVbd68WVWqVMmZogEAtpWYKK1dKz32mFSjhvT++9Yh3oMPSgsWSGfOSP/7HyEeAAAAALtiF0GeJE2YMEEWi0ULFy5UUFCQDMOQZJ4W269fPyUlJal79+5q3LhxqnUtW7aUt7e3Pvroo1SvJyYmasCAAfr+++9VoUIFbd68WdWqVbPV2wEA5JTLl81QrmZNqXNn6fvvzRNpk7m5SSNHSvv2STt3SoMGSf8cogQAAAAA9sQubq2VpKZNm2ratGl67rnnFBAQoLfeektlypTRkSNHFBsbqzp16mj27NlW686cOaPTp0/r2rVrqV5ftmyZli9fLsk8FXfYsGHpXvvTTz9VkyZNcvT9AACywTDMZ97NmCEtWyaldap57drms++GDJFKlrR5iQAAAACQ0+wmyJOk8ePHq2HDhpo6dap2796tS5cuycvLS7169dIrr7wiDw+PTO8VGxub8nloaKhCQ0PTnXv9+vXslA0AyClRUeapszNmSL/9Zj3u6Ch162YGeG3amIdZAAAAAEABYVdBniT5+fnJz88v0/PTC+iGDh2qoUOH5kxRAIDc9ccf0syZ0rx50o0b1uMVK0qjRpkfPOsUAAAAQAFld0EeAKCQiI+XVq82u+/+OdDIyiOPmN133bpJTk62rQ8AAAAAbIwgDwCQv5w7J82eLQUFmZ/frlgx87l3Y8ZI995r+/oAAAAAII8Q5AEA8p5hSD/9ZHbfff21lJhoPadRI7P7bsAAKQvPRAUAAACAgoIgDwCQd65flxYsMAO8P/6wHnd2lnr3NgO85s05vAIAAABAoUaQBwCwvd9+Mw+vWLRIio62HvfykkaPloYPl8qVs3l5AAAAAJAfEeQBAGwjNlZascLsvvvlF+txi0Xq2NHsvuvUSXJ0tH2NAAAAAJCPEeQBAHJXaKgUGCjNmSNduWI9XqqUNGKEFBAg1ahh8/IAAAAAwF4Q5AEAcl5SkrR+vdl9t3ateZjF7R54wOy+691bcnOzfY0AAAAAYGcI8gAAOefKFemLL6RZs6RTp6zH3dyk/v2lMWMkX1/b1wcAAAAAdowgDwCQPYYh7d5tdt8tW2Y+C+92tWqZ3XdDhkienravEQAAAAAKAII8AMDdiY6WvvrKDPD277ced3CQunUzA7w2bcyvAQAAAAB3jSAPAJA1R49KM2dK8+ZJ169bj5cvL/n7S6NGSVWr2rw8AAAAACioCPIAAHeWkCCtXm12323alPachx4yu++6d5ecnW1aHgAAAAAUBgR5AID0nT8vzZ4tBQVJZ89ajxcrJg0ebB5eUb++7esDAAAAgEKEIA8AkJphSFu3mt13X39tduPdrmFDs/tuwAAzzAMAAAAA5DqCPACA6fp1aeFCM8ALCbEed3KSevUyA7wWLSSLxfY1AgAAAEAhRpAHAIXdgQPm4RWLFklRUdbjVatKo0dLI0aYB1kAAAAAAPIEQR4AFEaxsdLKlWb33c8/pz2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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "x1 = np.linspace(100,250,500)\n",
    "plt.plot(x1,cdf(x1,b1,b2),c='red')\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"pdf(x)\")\n",
    "plt.title(r'$F(x) = {:0.5f}\\times (x-{}) $ '.format(1/(b2-b1),b1));\n",
    "bounds = np.array([175,200])\n",
    "cdfs = cdf(bounds,b1,b2)\n",
    "plt.scatter(bounds,cdfs);\n",
    "plt.plot([100,bounds[0]],[cdfs[0],cdfs[0]],'k')\n",
    "plt.plot([100,bounds[1]],[cdfs[1],cdfs[1]],'k')\n",
    "plt.plot([bounds[0],bounds[0]],[0,cdfs[0]],'k')\n",
    "plt.plot([bounds[1],bounds[1]],[0,cdfs[1]],'k')\n",
    "plt.text(95,cdfs[0]+0.03,'{:.4f}'.format(cdfs[0]));\n",
    "plt.text(95,cdfs[1]+0.03,'{:.4f}'.format(cdfs[1]));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a23af8f0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cdf(200) - cdf(175) = \n",
      "0.66667 - 0.45833 = 0.20833\n"
     ]
    }
   ],
   "source": [
    "print(\"cdf(200) - cdf(175) = \")\n",
    "print(\"{:.5f} - {:.5f} = {:.5f}\".format(cdf(bounds[1],b1,b2), cdf(bounds[0],b1,b2),cdf(bounds[1],b1,b2)-cdf(bounds[0],b1,b2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7f70a13-2c07-479e-9fd1-432f24014f08",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Loi Normale \n",
    "### Fonction de probabilité et d'échantillonnage\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3d41262b-b21a-4f5d-8ecc-77ab46b150cd",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "m = 180\n",
    "s = 20\n",
    "\n",
    "def f(x,m=0,s=1):\n",
    "    t = (x-m)/s\n",
    "    return 1/(s*np.sqrt(2*np.pi))*np.exp(-0.5*(t**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "988423f3",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "plt.plot(x1,f(x1,m,s),c='red')\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"pdf(x)\")\n",
    "plt.plot([m,m],[0,0.025],'k')\n",
    "plt.arrow(m,0.023,s,0,color='k',length_includes_head=True,shape='full',width=0.0005);\n",
    "plt.title(r'$X\\sim {\\mathcal {N}}(\\mu ,\\sigma ^{2}) = {\\mathcal {N}}(180 ,20 ^{2})$ ');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "123afc03-e5a2-467a-9ab3-719f26950e80",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Loi Normale \n",
    "### Fonction de probabilité et d'échantillonnage\n",
    "$f(x)={\\frac {1}{\\sigma {\\sqrt {2\\pi }}}}\\operatorname {e} ^{-{\\frac {1}{2}}\\left({\\frac {x-\\mu }{\\sigma }}\\right)^{2}}$ \n",
    "\n",
    "$f(x)={\\frac {1}{\\sigma {\\sqrt {2\\pi }}}}\\operatorname {e} ^{-{\\frac {1}{2}}{t}^{2}}$ avec $t = \\frac{x-\\mu}{\\sigma}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "d968901b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vto9VqWJGjjVq5FyuzMTHx2wQMmmSuS+ZHYG7dJF695aio53NBwAAshQaeQAAAJ5o+XLTxNuxwz722GNmbbeyZZ3LlVl16yatWiUVLGgf+/hjqVkz6fx553IBAIAshUYeAACAp1m0SHrooYQNpKFDpTlzpMBA53JldvXrm3XzatSwj61aJT3wgHTunHO5AABAlkEjDwAAwJP88IP06KNmeqck5cghffutNHiw5MWvdumuRAlp3TqpfXv72C+/SE2bmvUKAQAA0hG/7QEAAHiKBQvM9Nm4Jt4tt5hNLVq1cjRWlpM9uzRzpvT88/axTZuk+++XTp92LhcAAMj0aOQBAAB4gvnzpccftzdXyJnTNPHuvtvZXFmVl5fZBOOll+xjwcGmmXfqlHO5AABApkYjDwAAwN3NnSs98YR0+bKpc+eWVqyQ6tRxNFaW53JJH30k9eljH9uyRWrcWDp50rFYAAAg86KRBwAA4M6+/lpq106KiTF1njymiVerlrO5YLhc0ujRUr9+9rE//pAaNZJOnHAuFwAAyJRo5AEAALir//1P6tDBbuLlzSutXCkFBTmbCwm5XNKHH0r9+9vH/vpLuu8+6dgx53IBAIBMh0YeAACAO5o5U+rYUYqNNXW+fNKqVVL16s7mQuJcLun996UBA+xjW7eaZt7Ro87lAgAAmQqNPAAAAHczbZr09NN2E69AAWn1aqlaNWdz4fpcLmnYMGnwYPtYaKh0773S4cOOxQIAAJkHjTwAAAB38sUXUufOkmWZumBB08SrUsXZXEgel0saOlQaMsQ+tn27aeYdOuRUKgAAkEnQyAMAAHAXs2dLzz5rN/EKFTJNvNtvdzYXUu6tt6R33rHrnTvNBhinTjmXCQAAeDwaeQAAAO5gzRrpmWfsukgR6aefpNtucyoRUmvQIGn4cLvesUN65BEpMtK5TAAAwKPRyAMAAHBaaKjUqpV06ZKp8+UzI/EqVXI0FtLAG2+YqbZxNmxIuP4hAABACtDIAwAAcNLRo1Lz5tLZs6b295cWLpQqVnQ0FtLQoEHSc8/Z9Zw50muvOZcHAAB4LBp5AAAATgkLkx58UNq/39QulzRzplS3rrO5kLZcLmniRKlZM/vYyJHS+PHOZQIAAB6JRh4AAIATLl+W2raVQkLsY6NHS61bO5cJ6cfHR/rmG+nOO+1jvXpJCxY4FgkAAHgeGnkAAAAZzbKknj2lRYvsY717S336OBYJGeCWW6Qff5RKlDC1ZUnt20u//upsLgAA4DFo5AEAAGS0Dz6QJk+260cflUaNci4PMk7RotLixVKuXKaOiJBatpR273Y2FwAA8Ag08gAAADLS//5ndjKNU6eOWRcvWzbnMiFj3X67NH++mW4rSSdOmA1PTp50NhcAAHB7NPIAAAAyypo1UufOdl2unPT991L27M5lgjMaNZK++MKud+6UHnnEjNADAABIAo08AACAjLBtm9SqlXTpkqnz5zdTLAsUcDQWHPTUU9KwYXb988/S009LsbHOZQIAAG6NRh4AAEB6O3JEatFCOnvW1P7+ZiRe+fKOxoIbGDBA6trVrufOlfr3dy4PAABwazTyAAAA0lPcZgb795va5ZJmzZLq1nU2F9yDyyVNnCg1a2YfGzVK+uQT5zIBAAC3RSMPAAAgvViW9PzzUnCwfWzMGOmxx5zLBPfj7S19841Uvbp9rFcvM9UWAADgCjTyAAAA0sukSdK0aXb94otS797O5YH7uuUW6YcfpKJFTX35stSmjXT0qLO5AACAW6GRBwAAkB5+/dWMqopTr540erRzeeD+ihY1a+T5+Jj68GGpbVspOtrZXAAAwG3QyAMAAEhrx49LrVvbDZjChaU5c+wGDZCUunXN9Os4a9dKr7/uXB4AAOBWaOQBAACkpcuXpXbtpEOHTB23/lmRIs7mgud44QXpqafsevRo8x4CAABZHo08AACAtDRwoLR6tV2PHCk1aOBcHngel8usr1i1qn2sSxdp61bnMgEAALdAIw8AACCtzJsnjRhh1+3aJVwnD0iu7Nml+fOl3LlNffGi2e34/HlHYwEAAGfRyAMAAEgL//wjPfOMXd9xh/TZZ2Z0FXAzypWTZs606x07zHvMshyLBAAAnEUjDwAAILUuXDCjpcLCTJ0zpxmdlyOHs7ng+R58UHrzTbv+9tuEoz4BAECWQiMPAAAgNSzLrF8WGmofmz5dqlDBuUzIXN58U2rWzK4HDJBWrnQuDwAAcAyNPAAAgNQYPVqaO9euBwyQHnnEuTzIfLJlk2bNkkqXNnVsrFl/8cABR2MBAICMRyMPAADgZv30k/Taa3bdpIk0dKhjcZCJ5c1rNr/w9zf1yZPS449LUVHO5gIAABmKRh4AAMDNOHhQattWiokxdcmS0v/+Z0ZPAemhenXp00/t+rff2BUZAIAshkYeAABASl2+LLVvLx0/bmpfX7O5Rf78zuZC5tepk9Sjh11PnpxwZ1sAAJCp0cgDAABIqeHDpfXr7XrCBKlmTefyIGsZO1a66y67fuEFac8ex+IAAICMQyMPAAAgJTZskN5+266ffFJ67jnn8iDr8fOTvv5aypXL1BcuSB06SNHRzuYCAADpjkYeAABAcp09axp3sbGmLlNGmjjR0UjIokqVMtNq4/z6KxutAACQBdDIAwAASA7LMmuT7d9v6mzZzOYWOXM6mwtZ1xNPSJ072/W770pr1jiXBwAApDsaeQAAAMkxfbqZzhhn6FCpTh3n8gCS9PHHUvny5r5lSU89JZ0+7WwmAACQbmjkAQAA3MiuXVLPnnZ9zz3Sa685lweIExhoRoZ6e5v64EGpa1fT1AMAAJkOjTwAAIDruXRJat9eunjR1HnySDNmmKm1gDuoWdNMq40zf770+efO5QEAAOmGRh4AAMD1vPWWtHmzXU+ZIpUo4VweIDGvvCI1amTXvXtL//zjXB4AAJAuaOQBAAAkZdUq6YMP7LprV6l1a+fyAEnx8jIjRfPlM3V4uNShgxQV5WwuAACQpmjkAQAAJObkSaljR3utsYoVpTFjnM0EXE/RotIXX9j1li3SwIHO5QEAAGmORh4AAMDVLEt67jnp8GFT+/hIs2dLOXI4mwu4kYcfll54wa5HjZKWLXMuDwAASFM08gAAAK42aZK0YIFdv/++VL26c3mAlBg5UrrtNrt++mnp+HHn8gAAgDRDIw8AAOBK27ZJL79s102bSn36OBYHSLGAADOC1M/P1MeOSV262NPEAQCAx6KRBwAAECcyUmrf3nyVpAIFpGnTzEYCgCepWlX68EO7/vFHacIE5/IAAIA0wW+lAAAAcQYPlv78066//FIqXNixOECqvPii1KKFXb/yivTPP87lAQAAqUYjDwAAQJI2bDAbA8R56aWETRDA07hc0tSpUqFCpo6Kkjp1ki5fdjYXAAC4aTTyAAAALl6UnnnGXkOsYkXpgw8cjQSkiYIFpSlT7HrTJmnECOfyAACAVKGRBwAA8MYb0q5d5r6Xl1kXLyDA2UxAWmnZ0ozEizNkSMIp5AAAwGPQyAMAAFnb6tXSuHF23b+/dNddzuUB0sPYsVKxYuZ+dLRp7F265GgkAACQcjTyAABA1nXhgtSli13fcYcZrQRkNrlzS59/bte//y69+65TaQAAwE3yuEbe6tWr9dBDD6lAgQIKCAhQpUqVNHjwYF28eDHF11q4cKF69uypOnXqqHjx4vL391dgYKDuuOMO9enTR/v370+HVwAAANzGK69I+/aZ+97eZkqtn5+jkYB088ADUrdudv3uu1JwsHN5AABAinlUI2/cuHFq3LixfvzxR/n7+6ty5crat2+fhg0bplq1aun06dMput6oUaM0ceJEhYSEKFu2bKpSpYoKFCig0NBQffTRR7rtttu0bNmydHo1AADAUUuXSpMn2/XAgVKNGs7lATLCyJFS6dLmfkyMmWIbFeVoJAAAkHwe08gLDg5Wnz59JEmTJk3SgQMHFBISoj179igoKEihoaHq2rVriq7ZpUsXrVixQhcuXND+/fv122+/ae/evdqxY4caNmyo8PBwPfnkkzc12g8AALixs2elZ5+16+rVTSMPyOxuuUX64gu73rpVeust5/IAAIAU8ZhG3jvvvKPY2Fh17NhR3bp1k8vlkiQVLVpUs2fPlpeXl+bPn68/U7AD19NPP63GjRvL76opNOXKldM333wjSTp58qTWrl2bdi8EAAA4r08f6dAhc9/Hx0yp9fFxNBKQYe67T3rpJbv+8EPpl1+cywMAAJLNIxp5YWFhWrJkiSSp25XrevynfPnyatSokSRpzpw5afKchQoVUt68eSVJ4eHhaXJNAADgBr7/3jTu4rz9tlSlinN5ACe89550663mfmysmWLL77wAALg9j2jkbdmyRVFRUfLz81Pt2rUTPadBgwaSpF/S6NPE0NBQnT59Wl5eXqpevXqaXBMAADjs1KmEi/3Xri29+qpzeQCn5Mghffml9N8sF+3YwfRyAAA8gEc08nbs2CFJKlmypHySmPZSrlw5SdL27dtv+nksy9Lx48c1f/58Pfzww5KkV155RWXLlr3pawIAADfy4ovSsWPmvr+/GZnn7e1sJsAp9epJ/frZ9UcfSSwpAwCAW/OI31zjdqONm+qamLjHzpw5k+Lrz5w5Ux07dkxwrFKlSpo1a5Y6dOiQrGtMmjRJk6/c+e46QkNDU5wRAACk0ty50ldf2fW770qVKjmXB3AH77wj/fijFBoqWZb0zDPSn39KgYFOJwMAAInwiEZeZGSkJMnX1zfJc+I2rIiIiEjx9QsWLKh69eopNjZWBw8e1KFDh7Rjxw7NmjVLDRs2VPHixW94jSNHjigkJCTFzw0AADLA8ePS88/bdf36Uu/ezuUB3EXcyNS6daWYGGnvXql/f2niRKeTAQCARHhEI8/f31+SdOnSpSTPiYqKkiQFBASk+PpNmzZV06ZN4+s9e/aoX79++u6771SnTh1t3bpVuXLluu41ihQpoho1aiTr+UJDQ2+q4QgAAG6CZUk9ekgnT5o6e3azNli2bI7GAtxGrVrS66+bUaqS9Mkn0qOPSk2aOJsLAABcwyMaeXny5JFkT7FNTNxjceemRtmyZTV37lxVq1ZNW7du1fjx4zXwBov/du/eXd27d0/W9YOCghi9BwBARpkzR/r2W7seMUL6b21dAP95801p4UIzrVaSunaV/v6bKbYAALgZj9jsokKFCpKkAwcOKDo6OtFzdu/eneDc1MqWLZuaN28uSdq8eXOaXBMAAGSwU6fMBhdx7rsv4RRbAIavb8LNX/bvZxdbAADckEc08mrUqCFfX19FRUVp06ZNiZ6zbt06SVLdunXT7HnjmoaxsbFpdk0AAJCBXn5ZOnHC3A8IkKZMkbw84tcfIOPdeaf02mt2PW6ctHGjY3EAAMC1POI32cDAQD3wwAOSlOjOsDt37tSqVaskSY8//niaPOelS5f0ww8/SJKqV6+eJtcEAAAZaMkSacYMux42jCm1wI0MGmTv5mxZ0rPPSv+tRQ0AAJznEY08SRo8eLBcLpdmzJihyZMny7IsSWa32Pbt2ys2NlatWrVStWrVEnxf/fr1Vbp0aY0dOzbB8c2bN2vw4MHauXPnNc+1Y8cOtWzZUrt371ZgYKC6du2abq8LAACkgwsXpCvXrq1Vi11qgeTw95c++0xyuUwdGmpvggEAABznMY28WrVqafTo0ZLMxhKlSpVSjRo1VKZMGQUHB6tixYqaMmXKNd938OBB7d+/X2fPnk1wPCwsTMOGDVOFChVUsGBBBQUFqU6dOipVqpQqVqyoZcuWKW/evFqwYIGKFSuWES8RAACklQEDpAMHzH1vb+nzz9mlFkiuevWknj3t+r337E0wAACAozymkSdJffr00fLly9W8eXNdvHhR27ZtU6lSpTRgwABt3rxZ+fPnT/a1qlWrpo8//liPPfaYcufOrV27dik4OFgXL15U/fr1NWzYMG3fvl2NGjVKx1cEAADS3IYN0oQJdj1ggFSlinN5AE80fLhUsqS5f/my9NxzUkyMs5kAAIBcVtwcVWSYoKAghYSEqEaNGgoODnY6DgAAmUdkpFS9uvTPP6auXFnaskXy83M2F+CJliyRmje361GjpL59ncsDAEAmlZI+kUeNyAMAALiuYcPsJp7LZabU0sQDbk6zZlLHjnY9aJC0e7dzeQAAAI08AACQSfzxh/TBB3b90ktS3brO5QEygzFjpAIFzP2ICKlbN7ObLQAAcASNPAAA4PkuX5aefdZ8laRSpdhpE0gL+fJJ48fb9apV0hdfOJcHAIAsjkYeAADwfGPGSFeuJzJ5shQY6FweIDNp00Z6+GG77tdPOnzYuTwAAGRhNPIAAIBn27VLevNNu+7USWra1Lk8QGbjckkTJ0o5c5r63DmpZ0+m2AIA4AAaeQAAwHPFxkrPPWd2q5WkggWl0aOdzQRkRsWKSSNH2vV330nz5jkWBwCArIpGHgAA8FyffSatWWPXEyZIefM6lwfIzJ57Trr3Xrvu2VM6fdqxOAAAZEU08gAAgGc6dEh69VW7btVKat3asThApudySVOmSP7+pj5+3KyXBwAAMgyNPAAA4Hksy4wGOn/e1LlymdF4LpezuYDM7tZbpXfesesvv5SWL3csDgAAWQ2NPAAA4Hm+/VZasMCuR42SihZ1Lg+QlfTpIwUF2XWPHlJ4uGNxAADISmjkAQAAz3LunPTSS3Z9771Sly6OxQGyHG9v6fPPpWzZTL1nT8JRegAAIN3QyAMAAJ5l4EDp8GFz39dX+vRTptQCGa1aNalvX7v+8EPpzz+dywMAQBZBIw8AAHiOjRuliRPtetAgqWJF5/IAWdlbb0llypj7MTFSt27mKwAASDc08gAAgGeIjjaNAssydeXK0muvOZsJyMpy5JA++cSuf/3VjJAFAADphkYeAADwDKNGSX//bdeTJ5uptQCc88ADUvv2dv3GG9KhQ87lAQAgk6ORBwAA3N/u3dLbb9t1t25S/frO5QFgGzNGypPH3L9wIeFmNAAAIE3RyAMAAO7NsqQePaTISFMXKiS9/76zmQDYChUym13E+fZbacEC5/IAAJCJ0cgDAADubdYsacUKu/7oI3v0DwD30KWL1LChXffsKZ0/71weAAAyKRp5AADAfZ06Jb38sl23aCE98YRzeQAkzuWSJk2y1608dMjsKg0AANIUjTwAAOC+Xn1VOnnS3M+eXZowwTQMALifSpWkAQPsevx4adMm5/IAAJAJ0cgDAADuafVqaepUux46VCpd2rE4AJLh9ddNQ08y61t26yZFRzubCQCATIRGHgAAcD+RkVL37nZdvbrUu7dzeQAkj5+fmWIb548/zK62AAAgTdDIAwAA7mf4cGnnTnPfy0uaMkXy9nY2E4DkadhQeu45ux4yRNq717E4AABkJjTyAACAe9m2TXr/fbvu1UsKCnIuD4CUGzFCKljQ3I+IkJ5/3ky1BQAAqUIjDwAAuI/YWDOlNm5NrZIlpXfecTYTgJTLk0f66CO7XrpU+uor5/IAAJBJ0MgDAADu4/PPpfXr7XrCBCkw0Lk8AG5e27ZSs2Z23bu3dPq0c3kAAMgEaOQBAAD3cOyY1L+/XT/+uPTQQ87lAZA6Lpc0caKUPbupT5wwu9oCAICbRiMPAAC4h379pLNnzf2cORNOywPgmcqUkd56y66nTJE2bHAuDwAAHo5GHgAAcN7y5dKsWXY9fLhUtKhzeQCknZdflqpUsesePex1MAEAQIrQyAMAAM6KjJReeMGua9Uyf+gDyBx8fKRJk8xUW0n6+29p1ChnMwEA4KFo5AEAAGcNHy7t2mXuZ8smTZ5svgLIPOrWlbp1s+uhQ6W9e53LAwCAh6KRBwAAnBMaKr3/vl337i3deadjcQCko/fekwoVMvcjIsxIXMtyNhMAAB6GRh4AAHCGZUnPP2+vlVWihPT2285mApB+8uSRxoyx6yVLpDlznMsDAIAHopEHAACcMW2atGaNXY8fLwUGOpcHQPpr105q0sSue/eWzp1zLg8AAB6GRh4AAMh4J09Kr7xi161aSQ8/7FgcABnE5ZI++UTy9zf10aPSwIHOZgIAwIPQyAMAABnv1VelU6fM/cBA6eOPnc0DIOOUKycNGmTXEydKmzY5lwcAAA9CIw8AAGSsn36SvvzSrt95x6yPByDrePVVqXJlc9+ypO7dpcuXnc0EAIAHoJEHAAAyTlSU1KOHXVevLr34onN5ADjD11f69FO7/v13RuYCAJAMNPIAAEDGGTFC2r7d3PfykiZPlry9nc0EwBkNG0pdutj14MHSgQPO5QEAwAPQyAMAABlj507p3XftumdPqWZN5/IAcN6IEVL+/OZ+eLj00kvO5gEAwM3RyAMAAOnPsqTnnzdTayWpaFFp2DBnMwFwXr580qhRdv3999J33zkWBwAAd0cjDwAApL9Zs6SVK+3644+lnDmdywPAfXTsKN13n12/+KJ04YJzeQAAcGM08gAAQPo6fVrq29euH3xQeuwx5/IAcC8ul/TJJ2YDDEk6dMislwcAAK5BIw8AAKSv116TTpww9wMCpPHjzR/uABCnYkXp9dftetw4KSTEuTwAALgpGnkAACD9rF8vffaZXQ8ZIpUu7VQaAO7sjTek8uXN/dhYqVs3KSbG2UwAALgZGnkAACB9XLokde9u11WrSi+/7FweAO7N31/69FO7Dg6WJkxwLg8AAG6IRh4AAEgfo0ZJ27aZ+y6XNGmS5OPjbCYA7q1RI7P5RZxBg6SDB53LAwCAm/FOi4tcvHhRGzZs0MaNG3X48GGdOHFCkZGRypcvnwoUKKDKlSvrnnvuUYUKFdLi6QAAgLvbvVsaOtSue/SQ6tRxLg8AzzFqlPTjj2ajnAsXpN69pXnznE4FAIBbuOlGXnR0tObOnavJkydrw4YNirli/QrLsiRJrqsWsi5UqJA6dOigrl27qmLFijf71AAAwJ1ZlvTCC1JkpKkLF5aGD3c2EwDPUaCANGKE9Nxzpp4/X1q4UGrZ0tlcAAC4gRQ38iIiIjRq1Ch9/PHHOnXqVHzTztvbWxUrVlT+/PmVN29eBQQE6PTp0zp9+rT27t2rEydO6OjRoxozZozGjBmjRo0a6d1331Xt2rXT/EUBAAAHff21tGyZXY8dK+XO7VQaAJ6oc2dp2jRp3TpTv/iidN99UmCgs7kAAHBYihp5X375pQYPHqzDhw/Lsizdcccdat++vRo2bKigoCD5+/sn+b379u3Tr7/+qgULFuj777/XypUrtWrVKj3xxBMaMWKESpQokeoXAwAAHHb2rNSnj103ayY98YRTaQB4Ki8vs/HFnXdK0dHSgQNm1+uRI51OBgCAo1K02UWXLl104sQJdevWTVu2bNGff/6pN954Q/Xq1btuE0+SSpcurbZt2+p///ufjh8/ri+//FKVK1fW119/ralTp6bqRQAAADfxxhvSsWPmvr+/2XHyqqU2ACBZbrtN6t/frseOlX7/3ak0AAC4hRQ18rp3766dO3fqk08+UbVq1W76SbNnz66nn35af/31l7766iuVK1fupq8FAADcxMaNZgRNnLfeksqWdS4PAM83cKAU97dCTIzUvbv5CgBAFpWiqbWffPJJmj65y+XSE0y3AQDA80VHS9262fXtt0v9+jmXB0DmEBAgffKJ1LSpqTdtMh8Y9OzpbC4AABySohF5AAAAiRozRvr7b7ueNEny8XEuD4DMo0kTqUMHux4wQDp82Lk8AAA4yJFG3smTJ514WgAAkB727jWL0Mfp1k2qV8+xOAAyodGj7d2vz59PuKkOAABZSKobec2bN9eJEyeSff7y5ctVtWrV1D4tAABwB5YlvfiiFBFh6oIFpfffdzYTgMynUCHpgw/ses4cadEi5/IAAOCQVDfyli5dqmrVqmnZsmXXPe/y5cvq37+/mjdvrmNxu9kBAADPNnduwj+mx4yR8uRxLg+AzOu556S777brF16QLl50Lg8AAA5IdSOvbNmyOnr0qFq0aKFXX31Vly9fvuac3bt36+6779aoUaMUGxurtm3bpvZpAQCA086dk3r1suv775fat3cuD4DMzcvLrL/p/d9+ffv3S0OHOpsJAIAMlupG3u+//64nn3xSsbGxGj16tOrWravdu3fHPz59+nTVqFFDmzdvVvbs2fX555/rf//7X2qfFgAAOG3gQOnoUXPfz8/sLOlyOZsJQOZ2xx3SK6/Y9ahR0p9/OpcHAIAMlupGXmBgoGbMmKEvv/xSOXLkUHBwsKpXr67JkyfrqaeeUufOnXXhwgVVr15dwcHB6ty5c1rkBgAATtq4UZo40a4HDZJuvdW5PACyjsGDpTJlzP2YGLPBTkyMs5kAAMggabZr7dNPP62QkBDVrFlTYWFhev755zV79mxJUp8+ffTLL7+oQoUKafV0AADAKdHR5g9nyzJ15crSq686mwlA1pE9e8IPEn791YwIBgAgC0izRp4k3XrrrXrooYckSdZ/v9xXqVJFAwYMkI+PT1o+FQAAcMrIkdLff9v1lClmai0AZJRmzaQOHex6wADp4EHn8gAAkEHSrJF37NgxNWnSRG+//bYkqWbNmvL29tZff/2latWqacWKFWn1VAAAwCk7d0r//VsvSereXapXz7k8ALKuK3fJvnBBeuklZ/MAAJAB0qSRt3jxYlWtWlWrVq2Sj4+PRo4cqU2bNmndunUqXbq0jhw5ombNmql///6J7moLAAA8gGVJPXpIUVGmLlxYev99ZzMByLoKFjQjhON895307beOxQEAICOkupHXt29fPfTQQzpx4oTKlSunn3/+WX379pUk1a5dW7///rvat2+v2NhYjRo1SnXr1tWuXbtSHRwAAGSw6dOlVavsetw4KXdux+IAgDp3lu69165ffFE6d86xOAAApLdUN/LGjh0ry7LUsWNHbdmyRTVq1Ejw+C233KJZs2Zp6tSp8bvaXn0OAABwcydOSP99UCdJatlSat3auTwAIEkulzRpkr1O5+HDZr08AAAyqVQ38m655RbNnDlT06ZNU44cOZI8r1OnTgoJCVFQUJAuXryY2qcFAAAZqW9f6fRpcz8wUJowwfwBDQBOq1BBGjTIrj/5RPr5Z+fyAACQjlLdyAsJCVGHK3eMuo5bb71VGzduVL9+/VL7tAAAIKMsWybNnGnX774rlSjhXB4AuFr//tJtt5n7liV16yZduuRsJgAA0kGqG3nlypVL0fne3t4aMWJEap8WAABkhPBws8FFnFq1pJ49ncsDAInx9ZWmTLHrrVulDz90Lg8AAOkkTXatzUirV6/WQw89pAIFCiggIECVKlXS4MGDUzxd17Is/fzzz3r99ddVv3595cuXTz4+PipQoICaNm2qWbNmybKsdHoVAAB4iKFDpb17zf1s2cwfytmyOZsJABJz990JP3h45x1p507n8gAAkA5S1Mg7dOhQuoQ4cuRIss4bN26cGjdurB9//FH+/v6qXLmy9u3bp2HDhqlWrVo6Hbd2TzKsWrVK9erV0wcffKANGzYod+7cqlatmmJjY7V8+XI99dRTatmypaKiom72ZQEA4Nn++EMaOdKu+/WTqlVzLg8A3Mh770lFipj7UVFS9+5mqi0AAJlEihp5t956q3r16qXDhw+nyZPPnTtXVatW1ZQrh8EnITg4WH369JEkTZo0SQcOHFBISIj27NmjoKAghYaGqmvXrsl+bsuyVKZMGX300Uc6duyYdu/erc2bN+vUqVOaPn26/Pz89OOPP+qtt9662ZcHAIDniomRunY1XyWpTBmJfxMBuLvcuaVx4+x69Wpp2jTH4gAAkNZS1MgrWrSoxo8fr1tvvVXt2rXTwoULdfny5RQ94e7duzV06FBVqFBBbdu21bZt21S6dOkbft8777yj2NhYdezYUd26dZPrv53yihYtqtmzZ8vLy0vz58/Xn3/+mawctWvX1vbt29WrVy8VLFgwwWMdO3bUm2++KUmaMmWKYmNjU/QaAQDweBMmSL/9Zteffiplz+5cHgBIrscekx5+2K779ZOOH3cuDwAAacg7JSf/888/+vjjj/Xuu+/qm2++0Zw5c5Q7d27dddddql27tqpVq6YCBQoob9688vPz05kzZ3T69Gnt2bNHmzZt0q+//qp//vlHkhkR17RpU40cOVJ33HHHdZ83LCxMS5YskSR169btmsfLly+vRo0aacWKFZozZ46qVq16w9eSM2fO6z7evHlzDRw4UKdPn9aJEydUqFChG14TAIBM4cABacAAu37qKalpU+fyAEBKuFzS+PHSqlVSWJh0+rTUt2/C3bcBAPBQKWrk+fj4qF+/furSpYsmTZqkzz77THv27NGSJUu0dOnSG36/ZVny9fVVq1at1LNnTzVo0CBZz7tlyxZFRUXJz89PtWvXTvScBg0aaMWKFfrll19S8pKSFBkZGX8/ICAgTa4JAIDbsyyzK23cJlJ580qjRzubCQBSqkQJafhwqVcvU8+aJXXsKD3wgLO5AABIpZvatTZPnjx6/fXXtWvXLi1btkx9+/ZVUFCQvLy8ZFnWNbdChQqpTZs2mjhxov7991999dVXyW7iSdKOHTskSSVLlpSPj0+i55QrV06StH379pt5SdeYPXu2JKlatWo3HL0HAECmMXeu9MMPdj1qlFSggHN5AOBmvfCCdOUggB497A8pAADwUCkakZeY+++/X/fff78kKTo6WsePH9eJEycUGRmpfPnyqUCBAsqdO3eqniNuN9q8efMmeU7cY2fOnEnVc0lSSEiIPv30U0nS66+/nqzvmTRpkiZPnpysc0NDQ286GwAA6eb0aenFF+36vvukTp2cywMAqZEtmzR5shQUZDbu2bdPGjyYUcYAAI+Wokbe+fPn5eXlpcDAwEQf9/HxUbFixVSsWLE0CRcnbpqrr69vkuf4+flJkiIiIlL1XMeOHdOjjz6q6OhoPfroo2rXrl2yvu/IkSMKCQlJ1XMDAOCovn3tBeH9/aVJk8xaUwDgqapVk/r3l957z9Rjx0pPPCHVqeNoLAAAblaKGnm5c+dWkSJFdOjQofhjQ4cOVWBgoPr27Zvm4eL4+/tLki5dupTkOVFRUZJSt57duXPn1Lx5cx04cEBBQUH68ssvk/29RYoUUY0aNZJ1bmhoaKobjgAApKmlS6Vp0+z6nXek8uWdywMAaeXNN6V586QdO8w6oM8+K4WESP8NBAAAwJOkeGqtZVkJ6iFDhqhw4cLp2sjLkyePJHuKbWLiHos7N6XCwsLUrFkzbdmyRbfffruWLl2aorXxunfvru7duyfr3KCgIEbvAQDcx4UL0pW7wtesKfXp41gcAEhT/v7S559LcWt0b9tmRugNGeJoLAAAbkaKNrvw9fXVRQcWiK1QoYIk6cCBA4qOjk70nN27dyc4NyXCw8P14IMP6pdfflGFChW0YsUK5cuX7+YDAwDgSQYOlA4cMPe9vc0fvN6pXkYXANxH/fpmR+44w4dLf/3lXB4AAG5Sihp5xYsXV1hYmDZu3JheeRJVo0YN+fr6KioqSps2bUr0nHXr1kmS6tatm6JrR0ZG6pFHHtHatWtVunRprVy5UoULF051ZgAAPMKGDdL48Xb9xhtS1arO5QGA9PLee1KJEuZ+dLSZYhsT42wmAABSKEUft7do0ULjx4/Xfffdp6pVq8ZvenH69Gk1atQo2ddxuVxauXJlss8PDAzUAw88oIULF2ry5MmqV69egsd37typVatWSZIef/zxZF83OjparVu31ooVK1S8eHGtWrVKxYsXT/b3AwDg0SIjpeeeM2tGSVLlymZ0HgBkRrfcYjbxadHC1L/9Jn30kdnoBwAAD5GiRt7bb7+tdevW6Y8//tDmzZvjj1+6dEk//fRTsq/juokd8AYPHqwffvhBM2bMUL169dS1a1e5XC4dOXJE7du3V2xsrFq1aqVq1aol+L769evr4MGD6tOnj/pcsd5PTEyMnnzySS1atEiFCxfWqlWrVKZMmRTnAgDAYw0bJv3zj7nvcpkptSz+DiAza95c6thRmjHD1IMGSY88IpUr52wuAACSKUWNvDx58ig4OFjLly/XX3/9pfDwcA0ZMkSBgYHq169femWUJNWqVUujR49W37591b17dw0bNkz58+fXtm3bFBUVpYoVK2rKlCnXfN/Bgwe1f/9+nT17NsHxb775RnPmzJFkdsXt3Llzks89btw4Va9ePU1fDwAAjvr9d+mDD+y6Vy8phctTAIBHGjNGWrJEOnFCioiQunaVVq40H2gAAODmUryStZeXlx544AE98MADkhTfyHvrrbfSPNzV+vTpoypVqmjUqFH69ddfdfz4cZUqVUqPP/643njjjfipvskRFRUVf3/fvn3at29fkueeO3cuNbEBAHAvly+btaEuXzZ16dJmdB4AZAX58pm1Qdu2NfXq1dJnn5mGHgAAbi7VW9I9/fTTyp07dxpESZ7GjRurcePGyT4/qQbdM888o2eeeSZtQgEA4ElGj5ZCQux68mQpBR+GAYDHa9NG+t//pAULTP3KK2btvGLFnM0FAMANpLqR9+WXX6ZBDAAAkCF27JCuHEXfpYvUpIlzeQDACS6XNHGi9NNP0rlz0vnz0vPPm8YeU2wBAG7My+kAAAAgg8TGmqljkZGmLlxYGjnS2UwA4JSiRaVRo+x64ULpm2+cywMAQDKkaETe0KFD0+yJ33zzzTS7FgAASIbJk6W1a+164kQpTx7n8gCA07p0MVNsV60y9UsvSY0bS/nzO5sLAIAkpKiRN2TIELlSOdTcsiy5XC4aeQAAZKR//5X697frxx+XHn3UuTwA4A5cLmnKFOmOO8wOtidOSC+/LM2Y4XQyAAASlaJGXsOGDZNs5P3+++/xu7sWK1ZMxYsXlyQdOnRIBw8elCTlzp1b1apVS01eAACQUpZl1n66cMHUefJI48Y5mwkA3EXZstK770p9+5p65kypfXuz+QUAAG4mRY28n376KdHjb7zxhtasWaP27dtryJAhKl++fILHd+3apbfffluzZs1S3bp1NXz48JsODAAAUmjGDOnHH+16zBizPh4AwOjVS/rqK2nTJlN36yb9/beUO7ejsQAAuFqqN7uYN2+eRowYoRdeeEGzZs26poknSbfeeqtmzJihF154QR988IHmz5+f2qcFAADJceiQ+QM1TtOm0tNPO5cHANxRtmzS559LPj6mPnTITLEFAMDNpLqRN378eLlcLg0ZMuSG58adM378+NQ+LQAAuBHLMrvU/rf0hXLmlD77zKwJBQBI6I47pCv/pvnyS+mHH5xKAwBAolLdyPvzzz+VK1cu5U/Gzk758+dX7ty59ccff6T2aQEAwI188YW0eLFdjx0rlSjhWBwAcHv9+0u1atl1167S6dPO5QEA4CqpbuRFRUXp/PnzCgsLu+G5YWFhOn/+vKKiolL7tAAA4HoOHEg4LaxFC+mZZxyLAwAewdvbjMTz8zP10aMJlycAAMBhqW7kVaxYUbGxscmaLjt+/HjFxMSoYsWKqX1aAACQFMuSnn3W3qU2d25p8mSm1AJActx2m/TOO3Y9a5b07bfO5QEA4AqpbuR17txZlmVp0KBBevvttxMdmXfx4kUNHTpUgwYNksvlUufOnVP7tAAAICmTJkkrVtj1xx9LxYo5lwcAPE3fvlLdunbdo4d08qRzeQAA+I/LsiwrNReIjY1VixYttGzZMrlcLgUEBKhmzZoqVqyYXC6XDh48qM2bNysiIkKWZalJkyZavHixvLxS3UP0WEFBQQoJCVGNGjUUHBzsdBwAQGayd69UpYp08aKpH3nEjCRhNB4ApMyOHVK1alJkpKnbtpW++srZTACATCklfaJUd9O8vLz0/fffq0+fPsqWLZvCw8O1du1affXVV5o9e7bWrl2r8PBwZcuWTb169dL333+fpZt4AACkm9hYqUsXu4mXN6/06ac08QDgZlSoIL33nl1//bU0Z45zeQAAkOSdFhfx9fXV6NGj9eqrr2ru3LnavHmzjh8/LkkqWLCgatasqdatW6to0aJp8XQAACAxEyZIP/2UsC5c2LE4AODxevWS5s+X1q0z9fPPSw0bSoUKOZsLAJBlpUkjL06RIkX00ksvpeUlAQBAcuzaJb32ml23bm2mgQEAbp6XlzR1qlS1qhQeLp06ZZp58+Yx2hkA4Ig0beRJ0tatWxMdkXf77ben9VMBAABJiomRnnlGiogwdYEC0ief8EcmAKSFcuWkESOkF1809bffmrXy2rd3NhcAIEtKs0beDz/8oDfeeEPbtm1L9PHbbrtN7777rh5++OG0ekoAACCZXWk3bLDrTz4xzTwAQNqIG4W3erWpe/aU7r1XKlLE0VgAgKwnTXadGDp0qB555BFt3bpVlmUpW7ZsKliwoAoWLKhs2bLJsixt3bpVjz76qIYMGZIWTwkAACRp+3ZpwAC7btfOTKsFAKQdLy/piy+kwEBTnzkjde8uWZazuQAAWU6qG3lLlizRkCFDZFmWGjZsqGXLliksLExHjhzRkSNHFBYWpmXLlunee++VZVl65513tHTp0rTIDgBA1hYTI3XqJEVGmrpQIWn8eGczAUBmVbq0NHKkXS9cKM2Y4VgcAEDWlOpG3ujRoyVJbdq00erVq3X//ffL19c3/nFfX1/df//9Wrlypdq0aSPLsuK/BwAApMLIkdKvv9r1pElSvnzO5QGAzK5bN6lJE7vu1Us6eNC5PACALCfVjbzNmzfL5XJp9OjRcl1nUW2Xy6VRo0ZJkn777bfUPi0AAFnb779LgwfbdceO0iOPOBYHALIEl0v6/HMpZ05TnztnNhuKjXU0FgAg60h1I+/SpUvKnTu3ihUrdsNzixcvrjx58ig6Ojq1TwsAQNYVESE9+aQU9+9p0aLSRx85mwkAsooSJaSxY+165Ur+PxgAkGFS3cgrW7aswsLCdOnSpRueGxUVpbCwMJUtWza1TwsAQNb12mvSlbvET5sm5cnjXB4AyGqeeUZ69FG7fv116c8/HYsDAMg6Ut3I69Chg6KjozV9+vQbnjtjxgxFR0erQ4cOqX1aAACypiVLpHHj7LpvX+n++53LAwBZkcslTZ4sFSli6kuXzEjpuM2HAABIJ6lu5PXr10/169dXr169NG3atCTPmz59unr16qUGDRqoX79+qX1aAACynhMnpM6d7bpKFendd53LAwBZWf780pdf2vXff0tvvOFYHABA1uCd2gu89957atiwof766y916dJFb731lu69914VK1ZMLpdLBw8e1Jo1a3TgwAHlypVLDRo00PDhwxO91ptvvpnaOAAAZE6WZXZLPHrU1H5+0qxZkr+/s7kAICtr2lTq3dteI2/sWKlFi4Q72wIAkIZclmVZqbmAl5dX/G61cZe6evfapI5fLSYmJjVRPEZQUJBCQkJUo0YNBQcHOx0HAOAJPvtM6trVrseMkfr0cSwOAOA/ERFSrVrS1q2mLlrUrJeXL5+zuQAAHiMlfaJUj8hr2LDhDRt0AAAgFXbuNCM+4jRpIvXq5VweAIAtIED63/9MM+/SJenwYTOCeu5cs5YeAABpKNWNvJ9++ikNYgAAgERFR0tPPSWFh5s6b16zJpNXqpe5BQCklapVpffek+LWAp8/3/x/9ZXrmgIAkAb4KwAAAHf2zjvSpk12PWWKmbYFAHAvffpIjRvbda9e0u7djsUBAGRONPIAAHBXP/+ccFfazp2lxx5zLg8AIGleXmYUXp48pg4LMyOqL192NBYAIHOhkQcAgDs6f978ARgba+qyZe1dEQEA7ql4cWnSJLv+5ZeEH8gAAJBKNPIAAHBHvXtLe/ea+9mySTNnSrfc4mwmAMCNtWkjdepk1++8Yxp6AACkARp5AAC4m7lzzfSsOIMGSXXrOhYHAJBCH38slSlj7sfEmBHWFy44mwkAkCnQyAMAwJ0cOiR162bXd91lGnkAAM+RM6c0Y4a9w/ju3WYzDAAAUolGHgAA7uLyZalDB+nMGVPnyGGm1Hp7O5sLAJBy9epJAwfa9RdfSF995VweAECmQCMPAAB38fbb0tq1dv3RR9KttzqXBwCQOoMHS7Vr23XXrtLOnc7lAQB4PBp5AAC4gxUrEu5s2L691KWLc3kAAKnn42NG4eXKZeqwMOmJJ6TISGdzAQA8Fo08AACcduSI9OSTkmWZunx5adIkyeVyNhcAIPXKlDHTauP8/rvUr59jcQAAno1GHgAAToqJMU2848dN7ecnffONdMstzuYCAKSdxx6TXnzRridOlObMcS4PAMBj0cgDAMBJw4ZJq1fb9dix0p13OpUGAJBeRo6UatSw62efNbvZAgCQAjTyAABwyurVZoOLOE88IXXv7lweAED6iRtxnTOnqS9cMP+/HxXlbC4AgEehkQcAgBOOHZM6dLDXxStXTpoyhXXxACAzK1dO+uwzuw4JkV591bk8AACPQyMPAICMFhMjPfWUdPSoqX19E47SAABkXm3aSM8/b9fjxknz5zuXBwDgUWjkAQCQ0d57T1qxwq5HjUq4bhIAIHMbPTrheqhdukh79zoWBwDgOWjkAQCQkdaskd56y65bt5Z69nQuDwAg4/n7m5HYgYGmPndOattWunTJ2VwAALdHIw8AgIxy4oRZFy821tRlykiff866eACQFZUvL02ebNe//Sa99ppzeQAAHoFGHgAAGSE2VurYUTp82NQ+PmY0Rq5czuYCADinfXupa1e7HjtWWrDAsTgAAPdHIw8AgIwwYoS0dKldf/ihVLOmc3kAAO7ho4+kKlXs+plnpP37HYsDAHBvNPIAAEhvq1dLgwbZdatWUq9ejsUBALiRgAAzQjtHDlOfPWt2to2MdDQWAMA90cgDACA97d8vPfGEFBNj6lKlpC++YF08AICtUiXp00/t+rffpBdekCzLuUwAALdEIw8AgPQSESE99ph08qSp/fykuXOlPHmczQUAcD9PPSX16GHXU6dKn3ziXB4AgFuikQcAQHqwLPMHWUiIfWzSJNbFAwAk7aOPpLvvtuvevaX1653LAwBwOzTyAABID+PGSdOn2/VLL0mdOjmXBwDg/nx9zcjtIkVMffmy9Pjj0qFDzuYCALgNGnkAAKS1NWukvn3tumFDadQo5/IAADxHkSLSvHmSj4+pjx2TWreWoqKczQUAcAs08gAASEsHDpjdBuM2tyhe3OxGGPcHGQAAN1K3rjRhgl3/+qvUsyebXwAAaOQBAJBm4ja3OHHC1H5+0vz5UqFCzuYCAHierl2lbt3s+vPPpcmTncsDAHALNPIAAEgLliU9/7wUHGwf++QTqVYt5zIBADzbxx+b0XlxXnpJ2rDBuTwAAMfRyAMAIC1MmCBNm2bXPXtKnTs7lwcA4Pn8/MzmF4ULmzo62mx+cfiws7kAAI6hkQcAQGqtXSu9/LJd168vjR7tXB4AQOZRtKhp5sWttXr0qGnmsfkFAGRJNPIAAEiNgwfN5haXL5u6WDFpzhzJ19fZXACAzKNePTPNNs7GjVKvXs7lAQA4hkYeAAA3KzLSbG5x/LipfX2lefPsKVAAAKSV7t2l556z68mT2fwCALIgGnkAANyMuM0tfvvNPjZxonTXXc5lAgBkXi6XNH58wn9nXnyRzS8AIIuhkQcAwM147z3pyy/tukcP6dlnHYsDAMgC/PzMyO9ChUwdHS098oi0a5ezuQAAGYZGHgAAKTV7tjRwoF3Xry999JFzeQAAWUexYqaZF7cW66lT0oMPmq8AgEyPRh4AACmxfr30zDN2Xb689N13bG4BAMg49epJU6fa9Y4dZs1WdrIFgEyPRh4AAMm1a5fUqpV06ZKp8+WTfvzRfAUAICN16CANHWrXa9eazTAsy7lMAIB0RyMPAIDkOHVKatHCnrrk62tG4pUv72gsAEAWNmiQ1KmTXc+cKb39tnN5AADpjkYeAAA3EhUlPfqotHOnfezLL83aeAAAOMXlkiZPlu67zz729tvS9OnOZQIApCuPa+StXr1aDz30kAoUKKCAgABVqlRJgwcP1sWLF1N8raNHj2rmzJnq3bu36tWrp+zZs8vlcqlmzZrpkBwA4JEsS+rSRVq3zj42bJjUvr1zmQAAiOPraza/qFTJPvbcc9JPPzkWCQCQfrydDpAS48aNU+/evWVZlooXL64SJUpo27ZtGjZsmObNm6f169crb968yb7eV199pZdffjkdEwMAPN6QIdL//mfXzzwjDRjgVBoAAK6VJ49Zs7VOHenECSk62owk37gxYYMPAODxPGZEXnBwsPr06SNJmjRpkg4cOKCQkBDt2bNHQUFBCg0NVdeuXVN0zZw5c+r+++/X66+/rrlz52r48OHpkBwA4LGmT0+4kHijRtKkSWYqEwAA7qRsWen77yV/f1OfPSs9+KBp7AEAMg2PaeS98847io2NVceOHdWtWze5/vsjqmjRopo9e7a8vLw0f/58/fnnn8m+ZpcuXbR8+XK99957at26tYoUKZJe8QEAnuann8zUpDiVK5upS76+jkUCAOC66tSRZsyw6z17pEcekSIinMsEAEhTHtHICwsL05IlSyRJ3bp1u+bx8uXLq1GjRpKkOXPmZGg2AEAm9M8/ZkpSdLSpCxY0U5Zy53Y0FgAAN/T449IHH9j1xo1mWYjYWMciAQDSjkc08rZs2aKoqCj5+fmpdu3aiZ7ToEEDSdIvv/ySkdEAAJnN8eNSixZmSpJkpih9/71UpoyjsQAASLZXX5WuHADxzTfSwIHO5QEApBmPaOTt2LFDklSyZEn5+Pgkek65cuUkSdu3b8+wXACATObsWalZM2nvXvvYzJnSXXc5FgkAgBRzuaTx46WmTe1j778vjRnjXCYAQJrwiF1rT58+LUnX3ZE27rEzZ85kSKarTZo0SZMnT07WuaGhoemcBgCQYuHh0kMPSVu22MdGjJBat3YuEwAAN8vHx4zEq19f+vtvc6xvXylnTunZZ53NBgC4aR7RyIuMjJQk+V5ngXE/Pz9JUoRDC7keOXJEISEhjjw3ACCVLl2SHntM2rDBPtavn/TKK85lAgAgtXLlkpYskRo0sEebd+tmmnlt2jibDQBwUzyikef/3xbqly5dSvKcqKgoSVJAQECGZLpakSJFVKNGjWSdGxoa6ljDEQBwlZgY6cknpaVL7WPPPit9+KGZmgQAgCcrVkxascKMzDtyxGx68eST0i23mOUkAAAexSMaeXny5JFkT7FNTNxjcedmtO7du6t79+7JOjcoKIjRewDgDizLjEyYO9c+1qaNNGkSTTwAQOZRtqy0bJl0zz3S6dNmV/bHHjPH6td3Oh0AIAU8YrOLChUqSJIOHDig6OjoRM/ZvXt3gnMBALguyzLTZ7/4wj7WrJnZ3CJbNudyAQCQHu64Q1q8WAoMNHVEhPTggxIDDADAo3hEI69GjRry9fVVVFSUNm3alOg569atkyTVrVs3I6MBADzVsGEJd++rX1+aN0+6znqsAAB4tNq1pe+/l/5bX1znz0sPPCD984+zuQAAyeYRjbzAwEA98MADkpTozrA7d+7UqlWrJEmPP/54hmYDAHigjz+W3nzTrqtXl374Qcqe3blMAABkhPvuk+bMsUefnzwpNWki7d/vbC4AQLJ4RCNPkgYPHiyXy6UZM2Zo8uTJsixLktkttn379oqNjVWrVq1UrVq1BN9Xv359lS5dWmPHjnUgNQDA7UybJvXubdeVKpmNLnLlci4TAAAZqWVLafp0ez3Ygwel+++Xjh1zNhcA4IY8ppFXq1YtjR49WpLZWKJUqVKqUaOGypQpo+DgYFWsWFFTpky55vsOHjyo/fv36+zZs9c89u+//yp//vzxt5deekmS9McffyQ4PmLEiHR9bQCADDJ/vtSli12XKiUtXy4VKOBcJgAAnNChgzRhgl3v2iU1bSqdOeNcJgDADXlMI0+S+vTpo+XLl6t58+a6ePGitm3bplKlSmnAgAHavHmz8ufPn6LrxcTE6NSpU/G3sLAwSdLly5cTHA8PD0+PlwMAyEjLlknt2kmxsaYuVMg08YoXdzYXAABOef556b337PrPP6UWLaT//i4CALgfb6cDpFTjxo3VuHHjZJ+/b9++JB8rXbp0/BRdAEAmtmqV9OijUtzO53nymCZe+fLO5gIAwGmvvy6dOye9/76pf/lFeughs3Zs3A63AAC34VEj8gAASLGlS6UHH5TiRlfnyCEtWiRVqeJsLgAA3MXw4VKPHna9Zo3ZzfbcOecyAQASRSMPAJB5LVwoPfywFBlp6uzZpe+/l+rUcTYXAADuxOUy6+V16mQf+/lns5sta+YBgFuhkQcAyJzmzZMee0y6dMnUgYHSkiVSo0bO5gIAwB15eUlffCF17Wof++03qXFj6eRJ53IBABKgkQcAyHxmz5batpUuXzZ1rlxmTbwGDZzNBQCAO/Pykj79VHrxRfvYli3SffdJx445lwsAEI9GHgAgc5k2TXrySSkmxtR58kgrVzKdFgCA5PDykj7+WOrXzz7299/SvfdKhw87FgsAYNDIAwBkHpMnS507S3E7kufPL61eLQUFOZsLAABP4nJJH34oDRhgH/vnH+mee6R//3UuFwCARh4AIJMYP17q3t1u4hUqJP30k1StmqOxAADwSC6X9O670tCh9rFdu6SGDaW9e53LBQBZHI08AIDnGzVKeukluy5WTFq7Vrr9ducyAQCQGQweLL3/vl3v22eaeTt3OhYJALIyGnkAAM/27rvSK6/YdalSpolXoYJzmQAAyExee00aO9auDx40zbzQUMciAUBWRSMPAOCZLEsaOFAaNMg+VrastGaN+QoAANJO797SJ5/Y9dGjZs28kBDnMgFAFkQjDwDgeS5dkjp1koYPt49VqGBG4pUq5VwuAAAysx49pM8/N+vnSdKJE2Zk3uLFzuYCgCyERh4AwLOcOyc1by7NmGEfu/12MxKvWDHncgEAkBV06WL+Dc6WzdQXL0otW0pTpjibCwCyCBp5AADP8e+/Uv360qpV9rF775XWr5cKF3YsFgAAWcqTT0o//igFBpo6Jkbq1s0sdxG3ezwAIF3QyAMAeIY//pDq1JH+/ts+9uST0pIlUu7cjsUCACBLeuABs6RFkSL2sXfflZ5+2iyBAQBIFzTyAADub9kyqUED6fBh+9iAAWZqj5+fc7kAAMjKqleXfvnFLHERZ+ZMqVkz6exZx2IBQGZGIw8A4N6mTpUefFC6cMHU2bJJkyaZT/3jFtsGAADOKFnSLHFx7732sdWrzVIY//7rWCwAyKxo5AEA3JNlSUOGmEW1L182x3LkkL7/3qzDAwAA3EPu3GapiyeftI9t3WqWxPj9d6dSAUCmRCMPAOB+oqNNA+/tt+1jhQqZnWlbtHAuFwAASJyfn1nyYsAA+9jhw2ZpjKVLncsFAJkMjTwAgHs5d85Mpf3yS/tYpUpmDZ6gIMdiAQCAG3C5zNIXkyaZpTAkKSzM/Lv++efOZgOATIJGHgDAffz9t1SrlrR8uX2sYUPp55+l0qUdiwUAAFKgWzezFEaOHKaOiZGee07q2ZMdbQEglWjkAQDcw9dfS3fdJe3caR9r187sWJsnj3O5AABAyrVoIa1dKxUubB+bONFsinHokGOxAMDT0cgDADgrOlrq29c07cLDzTGXy2x0MWuWWXMHAAB4nho1pF9/Tbg0xsaN5viaNc7lAgAPRiMPAOCcY8ek+++Xxoyxj+XOLf3wg/TWW5IX/0wBAODRSpaU1q+Xnn3WPnb8uNS4sfn337KcywYAHoi/kAAAzvj5Z/OJ/Nq19rFq1aTNm9mZFgCAzMTfX/rsM2nyZMnX1xyLiTEj8tu3NxtiAACShUYeACBjWZY0YYJZI+fwYft4x46muVeunGPRAABAOuraVVq3TipRwj729ddSnTrSjh3O5QIAD0IjDwCQccLDpU6dpBdfNGvjSZK3tzR+vDRtmpQ9u7P5AABA+qpdWwoOlho1so9t3Wp2rV+wwLlcAOAhaOQBADLGnj3S3XdLM2bYx4oUMYtd9+xpNrgAAACZX4EC0tKl0muv2cfOn5datZIGDjTTbgEAiaKRBwBIf7Nnmx3r/vjDPtawoRQSYpp7AAAga/H2lt5/X5o3TwoMtI8PH242wti/37lsAODGaOQBANLPmTNmEesOHaSzZ+3jL78srVghFS7sWDQAAOAGHntM+u03qVIl+9iaNVLVqtLMmexqCwBXoZEHAEgfK1ZIVapIX31lH7vlFjM6b/RoycfHuWwAAMB9VKokbdoktW1rHzt/3myE1batdOqUc9kAwM3QyAMApK2ICKlPH6lJE+nQIft4w4bSn39K7do5Fg0AALipuA/7Zs6UcuWyj8+ZYz4YXLrUuWwA4EZo5AEA0k5IiFkL76OP7GM+PtKIEdKqVVLp0o5FAwAAbs7lkp580nzwd++99vEjR6RmzaSXXpLCwx2LBwDugEYeACD1YmKk996T7rpLCg21j99xh1n35tVXpWzZnMsHAAA8R8mS0sqV0qhRkq+vfXz8eKlGDWnzZueyAYDDaOQBAFJnzx7pnnukAQOky5fNMZdL6tfPNPGqVXM2HwAA8DxeXlLfvqZpV7WqfXz7dqluXWnYMPv3DgDIQmjkAQBuTmys9OmnplG3YYN9vEQJ8yn6yJGSv79z+QAAgOerUsVshNG/v/mgUDINvMGDpQYNpK1bnc0HABmMRh4AIOW2bDGfhj//vBQWZh+PW9fmvvucywYAADIXPz/pgw+k1avNtNs4v/wi3Xmn9Npr0sWLjsUDgIxEIw8AkHznz0u9e0s1a5pPx+PkySN99ZXZaS53bsfiAQCATOyee8wHhp062ccuXzabat12m7RggXPZACCD0MgDANyYZUlffy1VqiR9/LGZVhunXTszraVtW+fyAQCArCFXLunLL6UffpBKl7aPHzggtWolPfywtG+fM9kAIAPQyAMAXN/OnVKzZqZhd+SIfbx8eWnZMmn2bKlIEefyAQCArOfBB80HiQMGSD4+9vGFC83ovPffly5dci4fAKQTGnkAgMRFRkpvv20WmV62zD7u52eO//mn1KSJc/kAAEDWlj279O670h9/SPfeax+PiJDeeEOqXl1as8axeACQHmjkAQCutXy5aeANGSJFRdnHH3hA+vtv6c032ZEWAAC4h8qVpVWrpOnTpQIF7OPbtpkGX6dO0vHjjsUDgLREIw8AYPvzTzNVpWlTadcu+3jRotI330iLF0u33upcPgAAgMS4XFLHjtL27VKPHqaOM326WRJk2DB2twXg8WjkAQDMotAdO0p33iktWmQf9/KS+vSRQkOlNm0S/lIMAADgbvLkkT75RPrlFzO1Ns7589LgweYDyU8+kaKjncsIAKlAIw8AsrITJ0yjrkIFaeZMszttnHr1pOBgacwYKWdOxyICAACkWO3a0qZN0kcfSblz28ePHpVeeMFsiPH111JsrGMRAeBm0MgDgKwoLEwaOlQqV878gnvlp9K33SYtWCCtW2dG6AEAAHgib2+pVy9pzx7ptdcSru+7a5fUrp1Uq5a0YoVzGQEghWjkAUBWcumSNH68aeC99ZZ04YL9WIkS0tSpZp28hx9mGi0AAMgc8uSR3n/fNO+6dpWyZbMfCwmRmjQxt+Bg5zICQDLRyAOArODyZTN1tnJl6aWXEu7cljevNHKktGOH9MwzCX+5BQAAyCyKFZMmT5b+/ltq3TrhYytWSDVrSm3bmt1uAcBN0cgDgMwsPFwaN84s7Nyxo5laEicgQBowwBzr1y/hdBMAAIDMqlIlae5csyHGvfcmfOybb6TbbzezEzZscCQeAFwPjTwAyIxOnZLeflsqWdKsDbN/v/1YtmxSjx7S7t3Su+9KuXI5lxMAAMApd90lrVolLV4sVauW8LGFC6X69c1t4UI2xQDgNmjkAUBmsn+/1Lu3aeANGWIaenG8vc2ovG3bpE8+kYoUcSwmAACAW3C5pGbNzFp5//ufdMcdCR/fsMGMzqtaVZo2zaw3DAAOopEHAJnBX3+ZJl25ctLHH5sptXGyZzfNvd27penTpQoVnMsJAADgjry8pPbtzaZfP/wgNWiQ8PGtW81awuXKSWPGSGFhjsQEABp5AOCpYmOl5culBx80nxLPnCnFxNiP588vDR0qHTggjR1rRukBAAAgaS6X+d1q7Vrp55+lRx5J+PjBg1Lfvub3qkGDpH//dSYngCyLRh4AeJqjR6X33jMbWDRtKi1alPDx0qWl8ePNNNvBg6V8+RyJCQAA4NHq1pW++84sS9Kli+TjYz925oxZa7h0aemhh6Tvv5cuX3YqKYAshEYeAHiC2Fhp2TLp8celEiXMbrN79yY8p1o1s7bLzp1Sz55mSi0AAABSp3Jl6fPPze9er7wiBQbaj8XGSj/+aEbulS4tvfWWmQ0BAOmERh4AuLOjR6Xhw83ouwcekObNS/hpr5eX+RR4yRJpyxaztou3t3N5AQAAMqtixaQPPzTTaT/4QCpbNuHjhw6ZZU1KlzbTcxcsYJQegDRHIw8A3M3ly6Yx17q1GX03cOC1o++KFze70u7bJy1caJp8LpcTaQEAALKW3Lml/v3NLIjly6U2bRJ+kGpZZumTVq2kUqXMUid79jiVFkAmQyMPANxBTIy0Zo30/PNS0aJS8+bS/PnXjr57+GGzk9q+fWbqRokSjkUGAADI0ry8pPvvl775xmyC8cEHZlfbKx0+LA0bZo7fdZc0erQ5FwBuEo08AHCKZUkbN0q9e5uG3L33Sp9+Kp04kfC8EiWkt982m1csWGCmamTL5khkAAAAJKJQITNKb8cOacUK6YknEm6OIUmbNkn9+pnf7erXN5uTHT3qTF4AHouFlAAgI1mWFBwsff21+fQ2qcWQfXykFi2kbt3MtFkadwAAAO7Py0tq3Njcjh+Xpk2TvvhC+uefhOdt2GBuvXtL99wjtWsnPfaYlD+/M7kBeAwaeQCQ3qKjzci7H380m1Xs3p34edmySU2aSG3bmjVVcufOyJQAAABISwULSq++ana6/esv80Hu118n/F0wNlZavdrcXnjBTNV95BGzzErp0o5FB+C+aOQBQHo4csRsWLFokVkE+dy5xM/z8jJTatu25VNYAACAzMjlkqpWNbdhw6SQELupd+XsjJgYaelSc5OkypXNDI0WLcxUXF9fZ/IDcCs08gAgLcTESL/+Ki1ebJp3ISHXP79+fdO8e/xxqXDhjMkIAAAAZ7lcUlCQuX3wgfTLL6ahN2eO2RjjSqGh5jZqlBQYaGZutGhhRusVK+ZMfgCOo5EHADfDsqRdu6S1a6WVK80np6dPJ32+n58ZedeihRl5V7x4hkUFAACAG3K5pLp1zW30aGn9erOx2aJF166pFxYmffutuUlmdF+zZub3y7vvlnLlyvD4AJxBIw8AkiM2Vtq61TTu4m432mWsZEmzw2yLFtJ990k5cmRMVgAAAHgWLy+pYUNzGzVK2rPHnumxapUUGZnw/D//NLcRI8z33nmn/f0NGrBcC5CJ0cgDgMRcvixt2WI37datk86cuf73eHubX5zi1jKpXNl80goAAACkRNmyUs+e5hYRIf30k2nqLVpkmnxXio01y7qEhEhjx5pjt91mN/YaNmQqLpCJ0MgDgNhYaccOKThY2rzZ3EJCpPDwG3/v7beb5l2TJmaXsZw50z8vAAAAso6AALMuXvPm0scfm99bFy82zb116xJf3mXbNnP79FNTlywp1axp1uaL+5ovX4a+DABpg0YegKwlNlbavfvapt2FCzf+Xi8vqXp1+5PN+vWZtgAAAICM43JJFSuaW58+5nfbbdvMDJI1a5Je/uXAAXObP98+VqbMtc293Lkz6pUAuEk08gBkXidOmHXtrrz98Yd07lzyvt/HR6pd227c3X03I+4AAADgPry8pDvuMLcXXki4IVvcbd++xL93715zmzPHPlaunFSlipl1EnerWNFs3AbALdDIA+D5Tp68tmG3bZtp5CWXy2XWtKtZ0/5E8s47pezZ0y02AAAAkKZcLql8eXN79llz7NAheyZK3O3kycS/f/duc/vuO/tYtmzSrbeapt5tt9kNvgoVaPABDqCRB8D9xcZKR46YXyp27bJ/wYi7f/Zsyq9ZsWLCpl316lJgYJpHBwAAABxVrJi5PfKIqS3LTLO9cqmZzZuT3tgtJkbavt3crpya6+UllShhRvHdeqv5euXtllvS/7UBWZDHNfJWr16tUaNG6ddff1VYWJhKlSqlNm3a6PXXX1eOHDnc5poAUuDyZbOWx7//mtvBg+brnj2mWbdnjxQZeXPXzpcv4dSAO+4wI+1y5UrTlwAAAAB4BJdLKlXK3B57zByzLDPN9vffE85y2b5dio5O/DqxsdL+/ea2atW1jxcsaDf1Spc2Tb/ixc3XEiXM7+MuV3q9SiDTclmWZTkdIrnGjRun3r17y7IsFS9eXAUKFNC2bdsUFRWlypUra/369cqbN6/j17yRoKAghYSEqEaNGgoODk7TawNuxbLMenRHj0rHjpnb4cPXNuyOHDGf9KVG3rzXDve//XbzCwS/IAAAAAApFx1tPli/ehmbHTvMh/GpERhoN/au/Fq4sLkVKmRuTN9FFpCSPpHHjMgLDg5Wnz59JEmTJk1S165d5XK5dPjwYT388MMKDg5W165dNW/ePEevCWRqliWdPy+dOmW2uT91ytxOnrQbdXG3uObdpUtp9/xXfqp39Y2GHQAAAJC2fHzMOtKVK0uPP24fj442m2hcveTN7t3Jn00TFib984+5XU/u3HZT78oGX8GCZvZN3C1vXvOVxh8yOY9p5L3zzjuKjY3V008/rW7dusUfL1q0qGbPnq1KlSpp/vz5+vPPP1W1alXHrgm4NcuSIiLMKLlz50xTLu5+Yre4Zt2VX1P7ydv15MuX8BO50qVZZwMAAABwNz4+9qYaV4tb3/rK5t7VM3KiopL/XGfPmtv27ck7P0eOhI29fPlMMzBXrhvfcuaUvD2mTYIsyiPeoWFhYVqyZIkkJWi4xSlfvrwaNWqkFStWaM6cOclquqXHNYFUiYkx/6BFRpqvUVGm6RYRIYWH2/evruPuh4WZ28WL9v3EjqV2CuvNyJYt4adocetiXD2Mnh1iAQAAAM/m5WVvsHHPPdc+bllmRs+Vjb0rG31xM3xuZkM7yfztc/Gi2dDjZvj7m2m/gYGmKRh3/+pjOXJIAQHmb5iAAPt2ZR1339/fjBSM++rry2wi3DSPaORt2bJFUVFR8vPzU+3atRM9p0GDBlqxYoV++eUXx66Jq1hW0rfY2IRfr3csubeYmOR/vXzZfI27XVlfff/yZTN0PLGvV96/dMncv3Qp6fvR0XaT7sqGXWSkMw221MidO+EnXYkNd4+7nzev+QcdAAAAQNbmckkFCphbjRpJnxcVlfjSPXH3T5xIuNzPzW6Od7XISHM7eTJtrpcUX1+7sXd1k8/Hx3xN6n7cV29vc9/bO+H9q49ly2buZ8tm366sr37Myyv5X5Nzc7nsr1feT+zY9W6Q5CGNvB07dkiSSpYsKR8fn0TPKVeunCRpezKH26bHNbOkP/6Qata8tlEH9+ftfeOh5XnyXLvmRNzQdIacAwAAAEgvfn5SyZLmlhwREXZT7+o1va+3nNC5c9KFC+n7WhITN+gDKXNlw69ePemnn5xOlOE84i/x06dPS9J1d4+Ne+zMmTOOXHPSpEmaPHlysp47NDQ0Wed5jPRcMy2r8/VNfGh2YseSM/w77pYrl/kePtUAAAAAkBkEBJjleooXT/n3xsSYZt65c/ayRDdasujixaSXPbryfni4mRmGtHHlf8ss2ovwiEZe5H9DZH19fZM8x++/nWkiIiIcueaRI0cUEhKSrOfOVJxqBCU2VPfKIb43Gv57vWHEVz+W1PDkq48lZ+hz3P2r10i4+n7cjemoAAAAAJC+smUzs45y506f61++fO3SSnH3r66vt0zT1ceuXu4pqWWhbrSk1JV1UstTJXbs6uWwMnp2XhY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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "x1 = np.linspace(-4,4,100)\n",
    "plt.plot(x1,f(x1),c='red')\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"pdf(x)\")\n",
    "plt.title(r'$X\\sim {\\mathcal {N}}(\\mu ,\\sigma ^{2}) = {\\mathcal {N}}(0 ,1)$ ');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7de48ee-bd11-4865-a7ea-e2a14ddae497",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Loi Normale \n",
    "- Distribution la plus répendue\n",
    "- Elle correspond à un grand nombre de phénomènes\n",
    "- Théorème central limite\n",
    "    - Intuitivement, il affirme qu'une somme de variables aléatoires indépendantes et identiquement distribuées tend (le plus souvent) vers une variable aléatoire gaussienne.\n",
    "  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59d92acb-b54c-4919-954a-4ee85b1f67a9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Théorème central limite : Planche de Galton\n",
    "![alt text](galton.png \"figure\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "591d1a56-5af2-4950-acd2-c4a79b1bc6c5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Expérience"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "30467493-860f-4d84-be89-d15b576853d7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def f(x,m=0,s=1):\n",
    "    t = (x-m)/s\n",
    "    return 1/(s*np.sqrt(2*np.pi))*np.exp(-0.5*(t**2))\n",
    "\n",
    "def weight_n_potatoes(N,m,s):\n",
    "    return np.random.randn(N)*s+m"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "956b4ae0-1a84-4470-9d24-143773d57e4a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Échantillonnage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "bb09a701",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 6\n",
    "x = weight_n_potatoes(N,m,s)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Nombre de pdt\")\n",
    "plt.hist(x,bins);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "554979e9",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 100\n",
    "x = weight_n_potatoes(N,m,s)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Nombre de pdt\")\n",
    "plt.hist(x,bins);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ae0e4497",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "N = 50000\n",
    "x = weight_n_potatoes(N,m,s)\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.xlabel(\"x = masse [g]\")\n",
    "plt.ylabel(\"Nombre de pdt\")\n",
    "plt.hist(x,bins);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c4ffe446",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.ylabel(\"Proportion de pdt\")\n",
    "plt.hist(x,bins,weights=np.ones(N)/N)\n",
    "plt.xlabel(\"x = masse [g]\");\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "3759c243",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.ylabel(\"Proportion de pdt\")\n",
    "plt.hist(x,bins,weights=np.ones(N)/N/(bins[1]-bins[0]));\n",
    "x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "plt.plot(x1,f(x1,m,s));\n",
    "plt.xlabel(\"x = masse [g]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fb4f763",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exercice\n",
    "\n",
    "- Quelle est la probabilité de récolter une pdt qui pèse 182 g?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "4f6fdc32",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(182) = 0.019847627373850592\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.ylabel(\"Proportion de pdt\")\n",
    "plt.hist(x,bins,weights=np.ones(N)/N/(bins[1]-bins[0]));\n",
    "x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "plt.plot(x1,f(x1,m,s)); plt.xlabel(\"x = masse [g]\");\n",
    "\n",
    "print('f(182) = {}'.format(f(182,m,s),180,20))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dd66f8c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exercice\n",
    "\n",
    "- Quelle est la probabilité de récolter une pdt qui pèse entre 175 et 200 g?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "152af3bd",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aire verte = 0.4384400000004384\n"
     ]
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "bins=np.linspace(120,240,25)\n",
    "plt.ylabel(\"Proportion de pdt\")\n",
    "plt.hist(x,bins,weights=np.ones(N)/N/(bins[1]-bins[0]));\n",
    "x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "plt.plot(x1,f(x1));\n",
    "plt.xlabel(\"x = masse [g]\");\n",
    "bins=np.linspace(175,200,6)\n",
    "a = plt.hist(x,bins,weights=np.ones(N)/N/(bins[1]-bins[0]))\n",
    "plt.show()\n",
    "\n",
    "print('Aire verte = {}'.format(sum(a[0]*5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "dabdcea5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aire = 0.44359795035925975\n"
     ]
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "\n",
    "x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "plt.plot(x1,f(x1,180,20));\n",
    "plt.xlabel(\"x = masse [g]\");\n",
    "plt.ylabel('pdf(x)')\n",
    "bins=np.linspace(175,200,6)\n",
    "x2 = np.array(range(175,200))\n",
    "plt.bar(x2,f(x2,m,s))\n",
    "plt.show()\n",
    "\n",
    "print('Aire = {}'.format(sum(f(x2,m,s))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d80545a5",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aire = 0.4400322039753208\n"
     ]
    }
   ],
   "source": [
    "plt.figure(figsize=[15,5])\n",
    "\n",
    "x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "plt.plot(x1,f(x1,180,20));\n",
    "plt.xlabel(\"x = masse [g]\");\n",
    "bins=np.linspace(175,200,6)\n",
    "x2 = np.linspace(175,200,25*100)\n",
    "plt.bar(x2,f(x2,m,s))\n",
    "plt.show()\n",
    "\n",
    "print('Aire = {}'.format(sum(f(x2,m,s))/100))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7d51306",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Fonction de répartition\n",
    "\n",
    "$$f(x)={\\frac {1}{\\sigma {\\sqrt {2\\pi }}}}\\operatorname {e} ^{-{\\frac {1}{2}}\\left({\\frac {x-\\mu }{\\sigma }}\\right)^{2}}$$\n",
    "\n",
    "$$t = \\frac{x-\\mu}{\\sigma}$$\n",
    "\n",
    "$$f(x)={\\frac {1}{ {\\sqrt {2\\pi }}}}\\operatorname {e} ^{-{\\frac {1}{2}}{t}^{2}}$$\n",
    "\n",
    "$$F(x) = \\int_{-\\infty}^{x} f(x)dx $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "d96c83a5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def figure1():\n",
    "    plt.figure(figsize=[15,5])\n",
    "\n",
    "    x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "    plt.plot(x1,f(x1,180,20));\n",
    "    plt.xlabel(\"x = masse [g]\");\n",
    "    bins=np.linspace(175,200,6)\n",
    "    x2 = np.linspace(175,200,50)\n",
    "    plt.bar(x2,f(x2,m,s))\n",
    "\n",
    "    plt.ylabel('pdf(x)')\n",
    "\n",
    "    import scipy.stats as st\n",
    "    plt.figure(figsize=[15,5])\n",
    "    x1 = np.linspace(m-4*s,m+4*s,200)\n",
    "\n",
    "    plt.plot(x1,st.norm.cdf((x1-m)/s));\n",
    "    plt.xlabel('Weight [g]')\n",
    "    plt.ylabel('cdf(x)\\n ')\n",
    "    bounds = np.array([175,200])\n",
    "    cdf = st.norm.cdf((bounds-m)/s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "620d586c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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e3t668sorJRVdOVjW8wyLtW7dWi1bttTRo0e1Y8cO+/MMS96aLEldu3ZVQECAJOnjjz+u1npjY2Mlnb8asiy//PJLhVdjriyz+fwpc01f4Vf8WQ8dOqSkpKQy+2RlZVV4ERkAAIDLRWgIAADQABWHfr/88ouWLVsmqfTzDIsVh4n/93//p9zcXIf9i7m7u2v8+PGSpPnz52v16tUXPX5lFhsZOXKkJCkpKUkfffRRqe2GYejFF1+s8HiVVRyGSlJ6enqNHUeSrr/+evvxyvtMb7zxRoWfBwkAAHC5CA0BAAAaoOLQLzs7W19//bWksq80LNm+aNEiSeWv3jt9+nS1adNGBQUFuuGGG/T66687LIqSkZGhpUuXauzYsRowYECFax0wYICuu+46SdLEiRM1b948WSwWSdKRI0c0evRorVq1Sr6+vhUeszLat28vT09PSdJ7771Xo1cb+vn56YknnpAkzZ49W48//rg9YM3MzNTLL7+sGTNmKDg4uMZqAAAAkAgNAQAAGqQrr7xSPj4+kooWMYmOjlZkZGSZfYtDw+LFTgYMGGBfabikkJAQLVu2TDExMcrOztajjz6qpk2bKjg4WIGBgQoKCtKwYcO0YMEC5efnV6reBQsWqGPHjsrJydH999+vRo0aKTg4WBEREfrkk0/0zjvvqEmTJpKKbr+uTr6+vhozZowk6fHHH5e/v79atWqlqKgoPfbYY9V6rOJjFF9d+eqrryo0NFQhISEKDg7WtGnTNHr0aN18882Sqv+zAgAAFCM0BAAAaIA8PT111VVX2d+Xd5WhVHSlXcmFTi68Nbmk6OhobdiwQQsWLNBNN92k5s2bKzs7W/n5+YqOjtaIESP0/vvv25+NWFFhYWFav369nnnmGbVv315ms1nu7u763e9+p+XLl2vixInKyMiQJAUFBVVq7Ir45z//qRkzZqhr166SpOTkZB06dEinT5+u9mO5u7vr008/1XvvvafevXvLx8dHBQUF6tmzp9577z0tWLDAfpt0TXxWAAAASTIZNf00ZwAAAKCG7d27V+3bt5dUFOhFREQ4uaLSxo0bp/nz52vs2LGaN2/eZY9jGIYiIyN15MgRLViwwH4VZFmuueYa/fTTT3r22Wc1Y8aMyz4mAABoeLjSEAAAAPXeSy+9JEnq3LlznQwMq9PChQt15MgRubu7a/Dgwc4uBwAAuChCQwAAANR5u3bt0gMPPKCff/5ZmZmZDu3333+/5s6dK0maNm2as0qssPnz58tkMslkMmnq1Kll9hk1apQ+++wzh9ufT5w4of/7v//TxIkTJUn33XefwsPDS+07fPhw+/g//fRTjXwGAADg+ko/wRoAAACoY/Ly8jRnzhzNmTNHkhQYGCir1aqcnBx7nylTplz0Vl1nCwwMVLNmzRzaAgICyuz73Xff6eOPP5ZUtBCLh4eH/ZmNUtFiNG+88UaZ+wYHB5c6jr+/f1VKBwAADRDPNAQAAPj/du7QSEIoiKLoM3gUcWDJBIMlKCRJjCEHNCl8CxIxuiPYralzImh9q17z7933nW3bchxHrutKay3v+2YYhkzTlHVdf2qqu+97Pp9PzvNMay3P86Tv+4zjmHmesyxLuq776zMBgB8mGgIAAAAAhZ+GAAAAAEAhGgIAAAAAhWgIAAAAABSiIQAAAABQiIYAAAAAQCEaAgAAAACFaAgAAAAAFKIhAAAAAFB8AQBEaz1aoF0bAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure1()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "adafc272",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [],
   "source": [
    "def figure1():\n",
    "    import scipy.stats as st\n",
    "\n",
    "    plt.figure(figsize=[15,5])\n",
    "\n",
    "    x1 = np.linspace(m-4*s,m+4*s,100)\n",
    "    plt.plot(x1,f(x1,180,20.));\n",
    "    plt.xlabel(\"x = masse [g]\");\n",
    "    bins=np.linspace(175,200,6)\n",
    "    x2 = np.linspace(175,200,50)\n",
    "    plt.bar(x2,f(x2,m,s))\n",
    "    plt.ylabel('pdf(x)')\n",
    "\n",
    "    plt.figure(figsize=[15,5])\n",
    "    x1 = np.linspace(m-4*s,m+4*s,200)\n",
    "\n",
    "    plt.plot(x1,st.norm.cdf((x1-m)/s));\n",
    "    plt.xlabel('Weight [g]')\n",
    "    plt.ylabel('cdf(x)\\n ')\n",
    "    bounds = np.array([175,200])\n",
    "    cdf = st.norm.cdf((bounds-m)/s)\n",
    "    plt.scatter(bounds,cdf);\n",
    "    plt.plot([100,bounds[0]],[cdf[0],cdf[0]],'k')\n",
    "    plt.plot([100,bounds[1]],[cdf[1],cdf[1]],'k')\n",
    "    plt.plot([bounds[0],bounds[0]],[0,cdf[0]],'k')\n",
    "    plt.plot([bounds[1],bounds[1]],[0,cdf[1]],'k')\n",
    "    plt.text(95,cdf[0]+0.03,'{:.4f}'.format(cdf[0]));\n",
    "    plt.text(95,cdf[1]+0.03,'{:.4f}'.format(cdf[1]));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "9950ec92",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure1()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40b98643-31c2-43c3-9470-be2bc71ec7b4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "#### Avec F(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "63d21183-b696-4ff4-bab5-47becbb0a2a1",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'function' object is not subscriptable",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[52], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcdf[1]-cdf[0] = \u001b[39m\u001b[38;5;132;01m{:.6f}\u001b[39;00m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mformat(\u001b[43mcdf\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[38;5;241m-\u001b[39mcdf[\u001b[38;5;241m0\u001b[39m]))\n",
      "\u001b[1;31mTypeError\u001b[0m: 'function' object is not subscriptable"
     ]
    }
   ],
   "source": [
    "print('cdf[1]-cdf[0] = {:.6f}'.format(cdf[1]-cdf[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "430a34d5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Dans les tables de variable normale réduite: \n",
    "\n",
    "$p(175<x<200) = p(\\frac{175-180}{20}<t<\\frac{200-180}{20}) = p(-0.25<t<1)$\n",
    "\n",
    "0.0987 + 0.3413 = 0.44"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61f9e646-9493-423e-bb47-b681466b9ac8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Merci !"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  },
  "toc-showtags": false
 },
 "nbformat": 4,
 "nbformat_minor": 5
}