mharias/varianza.ipynb

## varianza.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con un poco de código Python vamos a demostrar que la $Var[aX]=a^2Var[X]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import uniform\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(threshold=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Partimos de una variable aleatoria $X$ que tiene una distibución uniforme $U[0,1]$ entre cero y uno, de la que extraemos 1000 valores, que guardamos en un `array` r:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "numero_muestras=1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "muestras = uniform.rvs(size=numero_muestras)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculamos su media y varianza:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5085521537909672"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "muestras.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5085521537909672"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "muestras.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08833681706411103"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "muestras.var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Que obviamente se acerca a los valores teóricos 1/2 y 1/8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veamos un gráfico con los valores y un histograma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "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": [
    "x = np.linspace(0,numero_muestras, numero_muestras)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(x, muestras,'r-', lw=5, alpha=0.6, label='uniform pdf')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "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": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(muestras, density=True, histtype='stepfilled', alpha=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y ahora construyamos una segunda variable aleatoria `W`, igual a dos veces `X`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "muestras_2=2*muestras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y calculamos su media, varianza:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0171043075819344"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "muestras_2.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.35334726825644414"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "muestras_2.var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Efectivamente se cumple que $E[W]=E[2X]=2E[X]$ y que $Var[W]=Var[2X]=4Var[X]$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "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": [
    "x = np.linspace(0,numero_muestras, numero_muestras)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(x, muestras_2,'r-', lw=5, alpha=0.6, label='uniform pdf')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "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": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(muestras_2, density=True, histtype='stepfilled', alpha=0.2)\n",
    "#ax.hist(r*2, density=True, histtype='stepfilled', alpha=0.2)\n",
    "plt.show()"
   ]
  }
 ],
 "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": 4
}