{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Illustration de la loi forte des grands nombres"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Loi uniforme sur [0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N = 10000 # nombre de tirages\n",
    "X = np.random.rand(N)\n",
    "\n",
    "integers1toN = np.arange(1,N+1) # un array contenant les entiers de 1 a N\n",
    "\n",
    "moyenneEmp = ??? # calculer pour n allant de 1 a N, (sum_{i=1}^n X_i)/n\n",
    "\n",
    "# Affichage\n",
    "fig = plt.figure()\n",
    "plt.plot(integers1toN, moyenneEmp, color=\"b\", label=\"Moyenne empirique\")\n",
    "plt.axhline(0.5, color=\"r\", label=\"Esperance\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Loi exponentielle de parametre 1/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam = 0.1\n",
    "Y = ??? # simuler la loi exponentielle a partir de X\n",
    "\n",
    "moyenneEmp = np.cumsum(Y)/integers1toN\n",
    "\n",
    "# Affichage\n",
    "fig = plt.figure()\n",
    "plt.plot(integers1toN, moyenneEmp, color=\"b\", label=\"Moyenne empirique\")\n",
    "plt.axhline(10, color=\"r\", label=\"Esperance\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Loi non intégrable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Loi de densité $1_{x>1}/x^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Loi non integrable : loi de densite 1_{x>1}/x^2\n",
    "Y = ??? # verifier que 1/U avec U uniforme sur [0,1] a la bonne loi\n",
    "\n",
    "moyenneEmp = np.cumsum(Y)/integers1toN\n",
    "\n",
    "# Affichage\n",
    "fig = plt.figure()\n",
    "plt.plot(integers1toN, moyenneEmp, color=\"b\", label=\"Moyenne empirique\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Loi de Cauchy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loi non integrable : loi de Cauchy de parametre 1 \n",
    "Y = ???\n",
    "\n",
    "moyenneEmp = np.cumsum(Y)/integers1toN\n",
    "\n",
    "# Affichage\n",
    "fig = plt.figure()\n",
    "plt.plot(integers1toN, moyenneEmp, color=\"b\", label=\"Moyenne empirique\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.10.6"
  },
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