Clase 1 - Estadística.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Espacios muestrales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": [
    "X2=[2**i for i in range(0,3)]\n",
    "X6=[6**i for i in range(0,3)]\n",
    "\n",
    "plt.title('Tamaño de espacio muestral $\\Omega $')\n",
    "plt.plot(X2,label='$2^n$')\n",
    "plt.plot(X6,label='$6^n$')\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Función exponencial $y(x)=e^x$')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "Y=[np.exp(x) for x in range(0,10)]\n",
    "plt.plot(Y)\n",
    "plt.title('Función exponencial $y(x)=e^x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variables aleatorias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Ejemplo_: Lanzar una moneda 4 veces. $X$ es la variable aleatoria que cuenta el número de veces que sale sol (1).\n",
    "$\\left\\vert \\Omega \\right\\vert=2^4=16$\n",
    "\n",
    "Vamos a repetir los 4 lanzamientos un total de 20 veces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=np.random.randint(0,2,size=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La primera simulación es: [1 0 0 0] \n",
      " (águila,sol,sol,águila)\n",
      " X=2\n"
     ]
    }
   ],
   "source": [
    "print('La primera simulación es:',X,'\\n','(águila,sol,sol,águila)\\n','X=2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ensayo 1: \t[1 0 1 0] , X=2\n",
      "ensayo 2: \t[0 0 0 0] , X=0\n",
      "ensayo 3: \t[0 0 1 1] , X=2\n",
      "ensayo 4: \t[1 0 0 1] , X=2\n",
      "ensayo 5: \t[0 1 0 0] , X=1\n",
      "ensayo 6: \t[1 1 0 0] , X=2\n",
      "ensayo 7: \t[1 1 1 1] , X=4\n",
      "ensayo 8: \t[1 0 0 1] , X=2\n",
      "ensayo 9: \t[0 1 1 1] , X=3\n",
      "ensayo 10: \t[1 0 1 1] , X=3\n",
      "ensayo 11: \t[0 0 1 0] , X=1\n",
      "ensayo 12: \t[0 0 1 0] , X=1\n",
      "ensayo 13: \t[1 1 0 0] , X=2\n",
      "ensayo 14: \t[1 1 0 0] , X=2\n",
      "ensayo 15: \t[1 1 0 0] , X=2\n",
      "ensayo 16: \t[0 1 1 0] , X=2\n",
      "ensayo 17: \t[1 1 0 1] , X=3\n",
      "ensayo 18: \t[0 1 0 1] , X=2\n",
      "ensayo 19: \t[0 0 1 0] , X=1\n",
      "ensayo 20: \t[0 1 0 0] , X=1\n"
     ]
    }
   ],
   "source": [
    "Repeticiones=[np.random.randint(0,2,size=4) for i in range(20)]\n",
    "for i,evento in enumerate(Repeticiones):\n",
    "    print('ensayo {0}: \\t{1}'.format(i+1,evento),', X={}'.format(sum(evento)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Repeticiones=[np.random.randint(0,2,size=4) for i in range(10000)]\n",
    "X3=[r for r in Repeticiones if sum(r)==3] #Lista con volados donde cayeron 3 soles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si repetimos el experimento $10^4$ veces, en promedio un 25% saldrá 3 veces sol."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2523"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Histogramas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1587., 10929., 32941., 54647., 54825., 32663., 10837.,  1571.]),\n",
       " array([0, 1, 2, 3, 4, 5, 6, 7, 8]),\n",
       " <a list of 8 Patch objects>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eqBdJel+alkD4JrAlyWVJfgKYBfYP3JMkva9MxZRRVR1L8uvAHwPrgC9W1cGB25rE1ExfjTGtvdnX6k1rb/a1OtPa1w9NxU1lSdLwpmXKSJI0MANBkgQYCGs2rT+1keSLSY4k+ZuhexmV5NIkf5rkxSQHk9w+dE8AST6U5Jkkf9V9/fbQPY1Ksi7JXyb52tC9jEpyKMnzSZ5LMjd0P0uSfCTJo0m+3X/X/tUU9PSx/u+09Pp+ks8N3dc43kNYg/6pjf8J/BsWH5n9JvCZqnph0MaAJD8H/AB4sKquGrqfJUk2Ahur6ltJfhp4Frhx6P9mSQJ8uKp+kOSDwF8At1fV/xiyryVJ/jOwFTivqj41dD9LkhwCtlbVNHzR6oeS7AX+vKq+0E8s/mRV/f3QfS3pfzv+N4tfvP3boftZziuEtZnan9qoqj8D3hi6j+Wq6rWq+lavvw28CGwatiuoRT/ozQ/2ayo+JSXZDFwPfGHoXs4GSc4Dfg64H6Cq/mGawqBtA/7XNIYBGAhrtQl4dWR7gSn4x+1skWQG+ATw9LCdLOppmeeAI8ATVTUVfQG/C/wG8I9DNzJGAX+S5Nn+SZlp8M+Bo8B/62m2LyT58NBNLTMLfHnoJk7GQFibiX5qQydK8lPAV4DPVdX3h+4HoKreq6qPs/gN+WuSDD7VluRTwJGqenboXk7iuqr6WRZ/ofi2nqoc2nrgZ4F7q+oTwP8Fpun+3k8Anwb++9C9nIyBsDb+1MYa9Bz9V4AvVdUfDN3Pcj298A1g+8CtAFwHfLrn6h8GfiHJ7w3b0j+pqsO9PAJ8lcVp1KEtAAsjV3iPshgQ0+KXgW9V1etDN3IyBsLa+FMbq9Q3b+8HXqyq3xm6nyVJNiT5SK+fC/wi8O1hu4KquqOqNlfVDIt/v56sql8duC0Akny4Hwygp2R+CRj8qbaq+j/Aq0k+1qVtwOAPeoz4DFM8XQRT8tMVZ5tp/qmNJF8Gfh64KMkC8FtVdf+wXQGLn3g/Czzf8/UAv1lVfzhgTwAbgb399McHgH1VNVWPeE6hS4CvLmY864Hfr6o/GralH/qPwJf6g9p3gV8buB8Akvwki08l/oehe1mJj51KkgCnjCRJzUCQJAEGgiSpGQiSJMBAkCQ1A0GSBBgIkqT2/wAkqiW4ewsssgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=200000 #número de simulaciones\n",
    "n=7 #número de volados sucesivos\n",
    "Simulacion=[np.random.randint(0,2,size=n) for i in range(N)]\n",
    "\n",
    "#Histograma de la variable aleatoria X=#veces que sale águila\n",
    "plt.hist([sum(sim) for sim in Simulacion],bins=[i for i in range(n+2)],\n",
    "         align='left',histtype='barstacked',rwidth=0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Clasificarl los eventos según el número de águilas\n",
    "X=[[evento for evento in Simulacion if sum(evento)==i] for i in range(n+1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "De las 200000 simulaciones, salieron 32663 veces águilas, lo cual es una fracción de 0.163 de todos los eventos\n"
     ]
    }
   ],
   "source": [
    "x=5 #numero de veces que sale aguila (1)\n",
    "print('De las {0} simulaciones, salieron {1} '\n",
    "      'veces águilas, lo cual es una fracción de {2:.3f} de todos los eventos'.format(N,len(X[5]),len(X[5])/len(Simulacion)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La probabilidad teórica es de 0.164\n"
     ]
    }
   ],
   "source": [
    "print('La probabilidad teórica es de {:.3f}'.format(21/128))"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}