{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "import numpy as np\n",
    "import random\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.255\n"
     ]
    }
   ],
   "source": [
    "a = [1,2,3,-1,-2,-3,4,-2,-2]\n",
    "\n",
    "# version etendue\n",
    "\n",
    "b = np.random.choice(a, size = 200, replace = True)\n",
    "\n",
    "print(np.mean(a))\n",
    "print(np.mean(b))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0aPfu3Tp37pxu3rypc+fOaffu3erp6Wn20oC6ccEXqBEXfDEZcMEXyBkXfDGVEH+gRqVS\nSZ2dnSqXyxoeHla5XFZnZ6dKpVKzlwbUjbt9gBqtWbNGktTV1aX+/n4VCgX19PTcOg5MJuz5A8AU\nwp4/AGBMxB8AEkT8ASBBxB8AEkT8ASBBE/ZuH9tDkn7R7HUAY7hf0tvNXgRQxScjonW8QRM2/sBE\nZruvltvpgImKbR8ASBDxB4AEEX+gMdubvQAgC/b8ASBBnPkDQIKIP1AH2ztsX7R9otlrAbIg/kB9\n/l7SymYvAsiK+AN1iIgjki41ex1AVsQfABJE/AEgQcQfABJE/AEgQcQfqIPtXZJ+LOl3bA/a7mz2\nmoBG8AlfAEgQZ/4AkCDiDwAJIv4AkCDiDwAJIv4AkCDiDwAJIv4AkCDiDwAJ+n+MLmJyR4ksrwAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ca4cdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "m = []\n",
    "for i in range(1000):\n",
    "    m.append(np.mean(np.random.choice(a, size = 200, replace = True)))\n",
    "\n",
    "plt.boxplot(m);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0054400000000000013"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}