{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loi binomiale de paramètres n et p\n",
    "On répète n fois une expérience de Bernoulli. \n",
    "\n",
    "La probabilité de succès est p.\n",
    "\n",
    "X est le nombre de succès. X prend les valeurs k qui vont de 0 à n. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 5\n",
    "p = 0.6\n",
    "k = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P(X=k)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.010240000000000003"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "binom.pmf(k,n,p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P(X $\\leqslant$ k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.010240000000000003"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom.cdf(k,n,p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Diagramme en bâtons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "from pylab import plt\n",
    "import numpy as np\n",
    "fig,ax = plt.subplots(1,1)\n",
    "x = np.arange(n+1)\n",
    "ax.plot(x,binom.pmf(x,n,p),'ro',ms=0)\n",
    "ax.vlines(x,0,binom.pmf(x,n,p),colors='r',lw=10,alpha=0.5)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k P(X=k)\n",
      "0 0.010240000000000003\n",
      "1 0.0768\n",
      "2 0.23040000000000002\n",
      "3 0.3455999999999997\n",
      "4 0.2592000000000001\n",
      "5 0.07775999999999998\n"
     ]
    }
   ],
   "source": [
    "print(\"k\",\"P(X=k)\")\n",
    "for k in range(n+1):\n",
    "    print(k,binom.pmf(k,n,p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}