binomial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import comb as binomio_de_newton"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "P_n = [binomio_de_newton(n, q) * p**q * (1 - p)**(n-q) for q in range(n+1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "exps = [sum(choice((0, 1)) for _ in range(n)) for _ in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "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": [
    "plt.plot(P_n, '.-')\n",
    "plt.xlabel('Cantidad de éxitos')\n",
    "plt.ylabel('')\n",
    "plt.hist(exps, bins=range(n+1), density=True);\n",
    "plt.axis([0, 100, 0, 0.15])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.273390607896142e+150"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.5**500 / (0.5**1000)"
   ]
  },
  {
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}