R/clases/3_estadistica/2_distribuciones_comunes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Notas para contenedor de docker:**\n",
    "\n",
    "Comando de docker para ejecución de la nota de forma local:\n",
    "\n",
    "nota: cambiar `dir_montar` por la ruta de directorio que se desea mapear a `/datos` dentro del contenedor de docker.\n",
    "\n",
    "```\n",
    "dir_montar=<ruta completa de mi máquina a mi directorio>#aquí colocar la ruta al directorio a montar, por ejemplo: \n",
    "#dir_montar=/Users/erick/midirectorio.\n",
    "```\n",
    "\n",
    "Ejecutar:\n",
    "\n",
    "```\n",
    "VERSION=<versión imagen de docker>\n",
    "docker run --rm -v $dir_montar:/datos --name jupyterlab_prope_r_kernel_tidyverse -p 8888:8888 -d palmoreck/jupyterlab_prope_r_kernel_tidyverse:$VERSION\n",
    "\n",
    "```\n",
    "\n",
    "Ir a `localhost:8888` y escribir el password para jupyterlab: `qwerty`\n",
    "\n",
    "\n",
    "Detener el contenedor de docker:\n",
    "\n",
    "```\n",
    "docker stop jupyterlab_prope_r_kernel_tidyverse\n",
    "```\n",
    "\n",
    "Documentación de la imagen de docker `palmoreck/jupyterlab_prope_r_kernel_tidyverse:<versión imagen de docker>` en [liga](https://github.com/palmoreck/dockerfiles/tree/master/jupyterlab/prope_r_kernel_tidyverse)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para ejecución de la nota usar:\n",
    "\n",
    "[docker](https://www.docker.com/) (instalación de forma **local** con [Get docker](https://docs.docker.com/install/)) y ejecutar comandos que están al inicio de la nota de forma **local**. \n",
    "\n",
    "O bien dar click en alguno de los botones siguientes:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/palmoreck/dockerfiles-for-binder/jupyterlab_prope_r_kernel_tidyverse?urlpath=lab/tree/Propedeutico/R/clases/3_estadistica/2_distribuciones_comunes.ipynb) esta opción crea una máquina individual en un servidor de Google, clona el repositorio y permite la ejecución de los notebooks de jupyter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Run on Repl.it](https://repl.it/badge/github/palmoreck/dummy)](https://repl.it/languages/Rlang) esta opción no clona el repositorio, no ejecuta los notebooks de jupyter pero permite ejecución de instrucciones de Python de forma colaborativa con [repl.it](https://repl.it/). Al dar click se crearán nuevos ***repl*** debajo de sus users de ***repl.it***.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lo siguiente está basado en los libros:\n",
    "\n",
    "### * B. Rumbos, Pensando Antes de Actuar: Fundamentos de Elección Racional, 2009\n",
    "\n",
    "### * G. J. Kerns, Introduction to Probability and Statistics Using R, 2014.\n",
    "\n",
    "### El libro de G. J. Kerns tiene github: [jkerns/IPSUR](https://github.com/gjkerns/IPSUR)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Nota:**\n",
    "\n",
    "* En algunas líneas no es necesario colocar `print` y sólo se ha realizado para mostrar los resultados de las funciones en un formato similar al de R pues la nota se escribió con *jupyterlab* y *R*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=5, repr.plot.height=5) #esta línea sólo se ejecuta para jupyterlab con R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Motivación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el análisis estadístico de datos de poblaciones aparecen ciertas distribuciones con mucha frecuencia. En lo que continúa se estudiarán tres de las más comunes: la distribución uniforme (discreta y continua), que representa datos equiprobables, la distribución binomial y la distribución normal, que están íntimamente relacionadas y podemos pensar a la segunda (normal) como la versión continua de la primera (binomial). Ésta última es muy importante en la práctica y en la teoría."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $X$ es una variable aleatoria con función de distribución -o densidad en el caso continuo- $f$, entonces decimos que los datos representados por los valores que toma $X$ tienen una distribución dada por $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Caso discreto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el caso discreto, en el cual $X$ toma valores $x_1,x_2,\\dots,x_n$ (soporte de $X$, $S_X$), éstos representan datos con media: $$\\mu = E(X) = \\displaystyle \\sum_{i=1}^nx_if(x_i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "en donde, recordemos que $f(x_i) = P(X = x_i)$ es la probabilidad de que $X$ tome el valor $x_i$. Asimismo, la varianza está dada por: $$\\sigma^2=E((X-\\mu)^2) = \\sum_{i=1}^n(x_i-\\mu)^2f(x_i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "que es el valor esperado de las desviaciones -al cuadrado- alrededor de la media. Decimos que la distribución $f$ tiene media $\\mu$ y varianza $\\sigma^2$. Claramente la desviación estándar es simplemente $\\sigma = \\sqrt{\\sigma^2}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Observación**\n",
    "\n",
    "La varianza de una variable aleatoria puede ser calculada con la fórmula: $\\sigma^2 = E(X^2)-(E(X))^2$.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Caso continuo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el caso continuo, en el cual $X$ toma valores en un intervalo de la forma $[a,b]$ o $(a,b)$ (soporte de $X$, $S_X$) o uniones de estos intervalos, éstos representan datos con media: $$\\mu=E(X)=\\displaystyle \\int_{X \\in S_X}xf(x)dx.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "si $\\displaystyle \\int_{X \\in S_X}|x|f(x)dx < \\infty$ (es finita)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Asimismo, la varianza está dada por: $$\\sigma^2=E((X-\\mu)^2) = \\int_{X \\in S_X}(x-\\mu)^2f(x)dx,$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y la desviación estándar es: $\\sigma = \\sqrt{\\sigma^2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Uniforme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuando los datos de un conjunto **ocurren, cada uno con la misma frecuencia**, decimos que están uniformemente distribuidos. Éste es el caso de la distribución de probabilidad determinada por una **variable aleatoria sobre un espacio muestral de datos equiprobables**. Por ejemplo, los que resultan de lanzar una moneda, lanzar un dado, girar una ruleta o bien, elegir un número al azar en el intervalo $[0, 1]$. La distribución que resulta, ya sea en el caso discreto o continuo, se conoce como distribución uniforme."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Su distribución de probabilidad: caso discreto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el caso discreto, dada una variable aleatoria $X$ que toma valores $\\{1, 2, \\dots , n\\}$, cada uno con probabilidad $\\frac{1}{n}$ , la distribución de probabilidad está dada por: $$f(i) = P(X=i)= \\frac{1}{n} \\forall i=1,2,\\dots,n.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Su gráfica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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QELWOI8sIAlBSxgAUsKWMASAxawxHlg\nAUsKWMAClhSwgCUGLGCJ88AClhSwgAUsKWABSwxYwBLngQUsKWABC1hSwAKWGLCAJc4DC1hS\nwAIWsKSABSwxYAFLnAcWsKSABSxgSQELWGLAApY4DyxgSQELWMCSAhawxIAFLHEeWMCSAhaw\ngCUFLGCJAQtY4jywgCUFLGABSwpYwBIDFrDEeWABSwpYwAKWFLCAJQYsYInzwAKWFLCA5bmK\nPalrdHEfx/mgzwUayv3N1+m9/hao3edvvlpX+lugqtrf/D5dI27fmzFYNS4KurmT07zvBXzO\nN+pafws01Pmbr9d+F6j3N1+nG+QdGYPFU6GrBXgqBJYQsIAlBixgifPAApYUsIAFLClgAUsM\nWMAS54EFLClgAQtYUsAClhiwgCXOAwtYUsACFrCkgOUR1hfAchWwPMJqP/BPDcBKHbA8wiro\nrI568HNgpQpYXl9jfTvjNJVzxZv1wHIMWM148f7BmDx1xP1bgOUQsJr1XeHeUcr4slUCrKQB\nqxmwvv7NSarL6Fu6tnseWMkClldYjUuGdlB9Z+zReveFPYGVLGB5hPVwL5V7feg58HftgJUs\nYHmEpU588pvw9U9+AaxkAcsjrLebZQlY3hdoY7AGfGJfLh8ALKeA5fWp8G37cn7zfzQNLFcL\ntFFYz+UCyylgeYG1bs4cdd8cs2l9+gHLKWB5gTVJReq8EFhOAcsLrA1vvaWK3zJa9G55s10B\ny90CbQmW0aQtzRcFLC8LtDFYaQhYrhZoQ7Bmz24w/hcOWE4BywMspap19OU7sJwClgdYy5Y1\nGv8LByyngMVrLDFgAUucB1YrgjU7LmA5BSxPL95jA5ZTwPL04j02YDkFLF5jiQELWOI8sFoR\nLM68uw9YnHkXAxZn3sV5YLUiWGkKWK4WABawhIDlGdbGJ8be+sQmYDkHLI+wgne1M1+559wD\nLMeA5RHWk+q//rRp08IfqqnAcgpYHmEd9wPrb/nVnd8HWE4ByyOsjjPsy+kdgeUUsDzCOvYx\n+3LyccByClgeYT3e62vzYmevx4HlFLA8wHrTaEG/bhNffnnid/stAJZTwOKNfmLAyiKs1+IC\nllPASsOPdNYUDRk9Lxi6saH4psD0+M1x+4HlcgFgrR80c+vy/DmhW+tmv1M4PW5z/H4Z1r9+\nfULuCVP+FbntBtb6Ud/L+8Gf5X3JYC35rwMOG/l3F4tHYe186qTcPo/ucDETbePPjso7/4+e\nRnYtv+jAHtd+GrnpBtbXM07OPfbBL8V9yWD9s7Bn57Nfc3E8MbDevfSgQ/M/cTETc2jP9e18\n3H3SoSWDFVz6yPhxZpEtxbcZH+YOq4lsKJoetzlxv/QZu8N62TYuctsFrO2nmCOdFos7k8Ba\n3smcOf7z1KtHYd1jHVph6pFoX/WzZjzJ+mtnc6TX5vBtN7Aesh5mlLgvCawd51ozv0+9eBTW\nB13NkSM3pp6JNsV6mGuEPUlg7f1BkxfvBS8aH0oDpQmwIptj9teXG+3+d5PWhtb8OLyhoel9\nEiu2R/qJOxsaxc0X2DMPpF69/pvQlX98x55ZlXom0lR75GQPI/++xJ65K3y7pjzlSFlHe+Yd\naWel3ittfs4e6Z36gCorw9eutGduTz0TaVtne+YvTXd9K8Man1Ncqha9e/nZWyNfwgLmmYcd\ngeh/AMWCFdkcu39Ff6MPdJMWhmC90XRX0kbZI99p9DBzgD2T72FkaejQ5nmYuSU0U+1hpoc9\n8lMPI38NPcyLHmbuCM3sTn3XSL3skYs8jHwYepgZTXdF/3nFweo9XFerVbrhrAnhLV5grR1r\n9FldkxaHjmNReEOw6X0SK7RH8sSdQS1uDv3Tuy716pEDeDt0aK+nnok0zh7pWO1h5mh7Zkj4\ndmN9ypH3Q4c2R9rZoBukzfYTu8opT7l6Q2T+xJD5lCPR1oUObVbTXbUyrA7P6lq1Uuvf9Ips\n8vBUaCW8ePj8UOswum0Jb3DxGutV+9CHijuTvMYqsGdmp1498hrry8OtkYM3pZ6J9Ef7YQZ6\nGNl1sz3zXPi2i9dYO3ra/2qVSjuTvMb6i/0wl6Q+oOhrrCJ7ZmrqmUg7+1gjXdY23ZXkNdbB\nT2ud+6rWszpFNqXjxfurucZh5M6P3HbzXeEY89CP3SDuSwKrzPqX7zoXi0dfvL/RxRjp9LKL\nmWi3mw/T0813n5G2ft96ko7cdvPi/c955tfF58V9yb4rnGA+zBHrUi8ehfWF9b3IwK9Tz0Rb\ndqB5aDOEPUlgnTlW63MHB+svif4Q2jydsMI8nVAysVLr2rKyW4vLNsdsjlxxgLXr4zuH3vlx\n9Kar81iv3Tz8se3yrmSnG758YsSYV92sHXMea+2EoXesdjMT05u3jyre5m3kq6dG/mxu9Kar\n81if3T103HvyrqTnsd669ZpHtrpYO+Z0w45p19/o7d+sXbtKH7juzpXSjiSw7ulRp19Qx/ZW\nj0a3rS66+sa5QeMleKBc67KA2aCYzdErDrAS4gRpWztBuucz4yntN6f0faj5/8lxYLlaoI3B\nSkPAcrUAsIAlBCx+/UsMWPz6lzgPrFYGi1//chew+PUvMWDx61/iPLBaGSx+/ctdwOLXv8SA\nxa9/ifPAakWwVFzAcgpY/PqXGLD4kY44D6zWB6t83Tof/0VoYLlcoK3B+sflOUrl/Hg9sBwD\nlkdYmw5R5xcWXqAOaf6PoYHlaoE2BmtEpyXmxZJOI4HlFLA8wuo+3r68owewnAKWR1gdfmtf\nPsvPCh0DlkdYva63L6/rDSyngOUR1nj1WLXW1ZPVncByClgeYX3bV+WdcXqeOvXbJmCAFROw\nvJ7H2vfQaV3zTnt4X7NdAcvdAm0LVuXdwt+KAVbTgOUNVrBDSVMpwGoasLy+573572oAlqcF\n2hish+xfpgBWioDlEdbve5/w2KvmW0nfBJZTwPIIi3eQugtYHmHxDlJ3AYt3kIoBC1jiPLBa\nHSz+2oybgMVfmxEDVtb/2syI5VvWv34ef23GOWB5PfNu/zd0Ggbw12YcA5bXd5B+bF++wDtI\nHQOWR1g9V9qXU/lrM44ByyOsiZdbPyvcedwTwHIKWB5hzT/y2Ifn/vcdB/Vf0OyfFwLL1QJt\nDFYa/uIMsFwt0MZgpeEvzgDL1QJtDFYaAparBYAFLCFgAUsMWMAS54EFLClgAQtYUsAClhiw\ngCXOAwtYUsACFrCkgAUsMWABS5wHFrCkgAUsYEkBC1hiwGp9sOoaUqdd3Mdx3u8CQb/zvg+g\n0d98o/a7gO8DkD+H0T+DxVesZsRXLJ4KxYAFLHEeWMCSAhawgCUFLGCJAQtY4jywgCUFLGAB\nSwpYwBIDFrDEeWABSwpYwAKWFLCAJQYsYInzwAKWFLCABSwpYAFLDFjAEueBBSwpYAELWFLA\nApYYsIAlzgMLWFLAAhawpIAFLDFgAUucBxawpIAFLGBJAQtYYsACljgPLGBJAQtYwJICFrDE\ngAUscR5YwJICFrCAJQUsYIkBC1jiPLCAJQUsYAFLCljAEgMWsMR5YAFLCljAApYUsIAlBixg\nifPAApYUsIAFLClgAUsMWMAS54EFLClgAQtYUsAClhiwgCXOAwtYUsACFrCkgAUsMWD9B8Ba\nUzRk9Lxg4q3xAbOrqvQi68paYHlbAFjrB83cujx/TuKt7WVGhQ9rvWikea0aWN4WAFbxbcaH\nucNqhFubAmsMWAXx9weWqwWAVfCi8aE0UCrcmjbGeE5cNLhgxF0lwPK4QJuHFQwsMD7uCJQ0\nvVWR/7rxcd2S9Z/OCCw0N6wda/RZXeqCLu7jOK/9LuBzvlHX+1zA53yDbvC5gM/5et0obq9N\nA6w3h+wJ32vKKPPjiv5GHzivR/t3jZFrzX4qDBY+GbnTwkB9+CpPha4WaPNPhclfvH8UxmY0\npSByFViuFgCWeYJhhXmCoWRiZcwtrR/5ubX/meWla6cH3gCWtwWApVcXXX3j3KD5dFcec0t/\nPWixtXtWYf6ICSujdweWqwWA5TVguVoAWMASAhawxIAFLHEeWMCSAhawgCUFLGCJAQtY4jyw\ngCUFLGABSwpYwBIDFrDEeWABSwpYwAKWFLCAJQYsYInzwAKWFLCABSwpYAFLDFjAEueBBSwp\nYAELWFLAApYYsIAlzgMLWFLAAhawpIAFLDFgAUucBxawpIAFLGBJAQtYYsACljgPLGBJAQtY\nwJICFrDEgAUscR5YwJICFrCAJQUsYIkBC1jiPLCAJQUsYAFLCljAEgMWsMR5YAFLCljAApYU\nsIAlBixgifPAApYUsIAFLClgAUsMWMAS54EFLClgAQtYUsAClhiwgCXOAwtYUsACFrCkgJV9\nWDUuCrq5k9O87wV8zjfqWn8LNNT5m6/Xfheo9zdfpxvkHRmDtffb1DW6uI/jfNDnAg17/M3X\n6XJ/C9RW+Juv1vv8LVBV5W++QleL28szBounQlcL8FQILCFgAUsMWMAS54EFLClgAQtYUsAC\nlhiwgCXOAwtYUsACFrCkgAUsMWABS5wHFrCkgAUsYEkBC1hiwAKWOA8sYEkBC1jAkgIWsMSA\nBSxxHljAkgIWsIAlBSxgiQELWOI8sIAlBSxgAUsKWMASAxawxHlgAUsKWMAClhSwgCUGLGCJ\n88AClhSwgAUsKWABSwxYwBLngQUsKWABC1hSwAKWGLCAJc4DC1hSwAIWsKSABSwxYAFLnAcW\nsKSABSxgSQELWGLAApY4DyxgSQELWMCSAhawxIAFLHEeWMCSAhawgCUFLGCJAQtY4jywgCUF\nLGBpvaZoyOh5wcRbiwJma5vsB5a7BYC1ftDMrcvz5yTeWjSyzKg6cT+wXC4ArOLbjA9zh9Uk\n3FpUIO4HlssFgFXwovGhNFCacGvR4IIRd5U02Q8slwu0eVjBwALj445AScKtdUvWfzojsDBu\n/+cvG23el7pGF/dxKhj0uUBjpb/5eu13gWp/87Xa7wK1/uardZ24vdIvLKspo+K2rOhv9KHz\nemnp2alZeBCnFkwub9kD+NvkDS17AGWT301xj2Y+FVotDNTHbtm5zGi3vExau+qyLDyIUxP7\n72zZA3ip/zstewDv9X8+xT2a+eLdakpB0xfv2QhY+wEs83TCCvN0QsnEyphbzywvXTs98EbM\nliwGrP0All5ddPWNc4Pm8155zK1ZhfkjJqyM3Z/FgLU/wCJqTsCijAQsykjAoozUimAte+D6\nYeOWhm9F31+RtRIeMuF9HVlovHUAV1WJh5PpNhTfFJhuXZPf8JJQK4J179w1f38hsDh0K/L+\niuwV/5CJ7+vIQtvNxy98WDycjLdu9juFFqwkb3hJqBXBsrrv/tCVyPsrslf8Q7bEqWGjTYE1\n4uFkoyILltM582itDdaEx0NXIu+vyF7xD5n4vo4sNW1M+Gkn+58BG5bTT/mitTJYywZvDF0L\nv78ii8U9ZMIP5LNVRf7r4uFkJQuW4/sSorUuWCvz43+oPmVU1g8h/JAtBOvNIXvEw8lK+y2s\nxfmr4jeY76/IcpGHbJGnwmDhk0kOJxvtr0+F84clfm9tvr8iy0UeskVevH+U+E8wq5+B/fTF\n+6zBi41vr7eF3mgReX9F9oo8ZPw7PbLZIz+3LlriM1BbVnZrcdnmpG94SagVwRppnRC8OfRG\ni+j7K7JW5CHj3+mRxb4eZJ/Ga4nPQJn16R+kk73hJaFWBItaU8CijAQsykjAoowELMpIwKKM\nBCzKSMBKU8vU7JY+hP+ogJWmgBUfsNIUsOIDVpoCVnzA8tpS9ah1eUPONr3n/nO6dTzmFxU6\nBGuqst43PKir+bH+ydNz8wYsMa/9um9eXp8b9rbYMbdAwPJaY8/jzYt9eZdq/Vn3sVOfvbbd\nj4ICrIYrcq6d8cTp7V7ReoIaOevFX/bb3qLHneWA5bn71N+Mj7PVXK1r6swNk9UyAdaz6iXj\nY92Zh9XrYy5quaNtqYDluY2q0Pg44MDQr/fVVZeqRwRY5/aoNntCfaj7Hb665Q63hQKW9y44\nqFpvaTfGvDr7/C7KaLwA60AVarFe3k0dPfKlSsdF97eA5b1Zar5+SJm/PvCkCrzyzqpFalwI\n1tM2rCtNWHnHr7L7Vuu9fxh7iurJayxyrLzzT4LHWq/gTznGfOvkygis/1HmN4H6RBPWmR0r\n4qbmq4lZP9IWDFjNaGT7+fY5h769641v/34SgfWB+aSoFygT1tPqFusNu19q/Y15uUWNabkj\nzn7AakZL1YE528wrD6lLZz159lkRWPq8nDFP/6zbqSas+oHqnMmzfnlpd6075Rf/7okT26f6\nQ8P7VcBqRo091aXWlfpHj+vYc/yWKKxtg/O6XvapfYK0ceZ5ebm9B8/R+r4LDu1w5OD3WvKQ\nsx6wKCMBizISsCgjAYsyErAoIwGLMhKwKCMBizISsCgjAYsyErAoIwGLMtL/A5zR6Qrfth5m\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n <- 10\n",
    "values <- 1:n\n",
    "probability <- 0.1\n",
    "qplot(values,probability,main='Uniforme discreta') #qplot is quick plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propiedades"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* $\\mu = \\displaystyle \\sum_{i=1}^ni\\frac{1}{n} = \\frac{n+1}{2}$.\n",
    "\n",
    "* $\\sigma = \\sqrt{\\displaystyle \\sum_{i=1}^n(i-\\mu)^2\\frac{1}{n}} = \\sqrt{\\frac{n^2-1}{12}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Su función de densidad: caso continuo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el caso continuo, considérese el caso de elegir un número al azar en el intervalo $[a,b]$ de la recta numérica. Sea $X$ la variable aleatoria asociada que toma cada uno de los valores del intervalo. La densidad de probabilidad correspondiente debe ser tal que el área bajo la gráfica sea la unidad y dados números $c$ y $d$ en el intervalo $[a, b]$, con $c < d$, la probabilidad: $$P(c < X < d) = \\frac{d-c}{b-a}$$ es el área por debajo de la gráfica entre $c$ y $d$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos definir esta función de densidad como: $$f(x) = \\begin{cases}\n",
    "\\frac{1}{b-a} & \\text{si } a \\leq x \\leq b,\\\\\n",
    "0 & \\text{en otro caso}\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La media y varianza están dadas por: $$\\mu=\\frac{a+b}{2},$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sigma^2=\\frac{(b-a)^2}{12}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Su gráfica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "n_runif<-500 #number of values\n",
    "a <- -2 #left point of interval\n",
    "b <- 3 #right point of interval\n",
    "vec <- seq(a,b,by=.01)\n",
    "dunif_value <- dunif(vec,a,b) #evaluating density function in vec\n",
    "                    #this evaluation is equal to 1/(b-a)\n",
    "df <- data.frame(valores=vec,probabilidad=dunif_value)\n",
    "gf <- ggplot(df, aes(x=vec,y=probabilidad))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hrttQ/0r/2CC6ypZtZu7LA1b4g5K2Pt9n0lax/y4/OdrQ9yVm5PWffy/unOXQYO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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_point(size=.5) + ylim(0, 1/(b-a)+.3)+\n",
    "ggtitle('Uniforme continua')+\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('runif')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El área debajo de la curva es: $$(b-a)\\frac{1}{b-a} = 1.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y la probabilidad de que $X$ esté entre $0$ y $2$ es el área formada en el rectángulo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WEfCotl/lZmvF1cOrBjx45XUnF1+QOx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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_point(size=.5) + ylim(0, 1/(b-a)+.3) +\n",
    "geom_segment(aes(x = 0, y = 0, xend = 0, yend = 1/(b-a))) +\n",
    "geom_segment(aes(x = 2, y = 0, xend = 2, yend = 1/(b-a))) +\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('runif')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Sea $X$ la variable aleatoria uniforme que representa el resultado observado al lanzar un dado. La probabilidad de observar del número $3$ en adelante es de: $$P(X\\geq 3) = \\displaystyle \\sum_{i=3}^6P(X=i)=\\sum_{i=3}^6\\frac{1}{6}=\\frac{4}{6}=\\frac{2}{3}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El lanzamiento medio es de: $$\\mu = \\displaystyle \\sum_{i=1}^6 i\\frac{1}{6} = \\frac{1+6}{2} = \\frac{7}{2} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "con desviación estándar:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sigma = \\sqrt{\\frac{(6-1)^2}{12}} \\approx 1.4.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) Sea $X$ el tiempo de espera (en minutos) en un consultorio dental y supongamos que éste sigue una distribución uniforme descrita por la función de densidad, $$f(x) = \\begin{cases}\n",
    "\\frac{1}{90} & \\text{si } 0 \\leq x \\leq 90,\\\\\n",
    "0 & \\text{en otro caso}\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La probabilidad de que un paciente espere entre $15$ y $45$ minutos está dada por: $$P(15 < X < 45) = \\frac{45-15}{90-0} = \\frac{1}{3}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**en R ...**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obsérvese que:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$P(15 < X < 45) = 1 - P((15 < X < 45)^c) = 1 - P( (15 < X)^c \\cup (X <45)^c)=$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$1 - P( X \\leq 15 \\cup 45 \\leq X) = 1 - (P(X \\leq 15) + P( 45 \\leq X))$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y la función [punif](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/Uniform) nos calcula $P(X \\leq 15)$ y si la volvemos a usar pero con el argumento `lower.tail=F` nos calcula $P(45 < X)$ que sí nos sirve pues como $X$ es **continua**: $P(X=45)=0$ (esto último no es igual para las variables discretas)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.333333333333333"
      ],
      "text/latex": [
       "0.333333333333333"
      ],
      "text/markdown": [
       "0.333333333333333"
      ],
      "text/plain": [
       "[1] 0.3333333"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_value <- 15\n",
    "right_value <- 45\n",
    "a<-0\n",
    "b<-90\n",
    "1-punif(left_value,a,b)-\n",
    "  punif(right_value,a,b, lower.tail = F) #same result using:\n",
    "                                         #1-punif(15,0,90)-punif(45,0,90)\n",
    "                                         #because is uniform distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El tiempo medio de espera es de: $$\\mu = \\frac{0+90}{2} = 45 \\text{ minutos}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "con desviación estándar: $$\\sigma = \\sqrt{\\frac{(90-0)^2}{12}} \\approx 26 \\text{ minutos}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binomial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La distribución binomial se basa en ensayos *Bernoulli* por ejemplo:\n",
    "\n",
    "* Se lanza un dado 10 veces, ¿cuál es la probabilidad de obtener 4 veces el número tres?\n",
    "\n",
    "* Un nuevo medicamento para la diabetes mantiene el nivel de glucosa en la sangre del paciente, muy cercano a los niveles normales. Desgraciadamente, el $10\\%$ de los pacientes que reciben este medicamento desarrolla hipertensión arterial. Un médico tiene $5$ pacientes diabéticos -sin relación alguna entre ellos- y desea saber la probabilidad de que todos ellos desarrollen hipertensión arterial si son tratados con el medicamento."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estas dos situaciones describen ejemplos de lo que se conoce como un **experimento binomial**: que consiste de $n$ **etapas o ensayos idénticos e independientes, llamados ensayos** *Bernoullli*, tales que:\n",
    "\n",
    "* En cada ensayo o etapa hay **dos posibles resultados**: éxito y fracaso (podríamos llamarlos positivo y negativo, o $1$ y $0$).\n",
    "\n",
    "* La **probabilidad de éxito** en cada ensayo es de $p$ y la de fracaso de $1-p$.\n",
    "\n",
    "La variable aleatoria discreta $X$ que asociamos a este experimento es el número de éxitos en los $n$ ensayos. En las situaciones descritas tenemos que,\n",
    "\n",
    "* $X$ cuenta el número de tres en $10$ lanzamientos de un dado.\n",
    "\n",
    "* $X$ cuenta el número de pacientes, del grupo de $5$ pacientes, que desarrollan hipertensión arterial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ¿Cómo obtenemos una distribución binomial?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pensemos ahora en lanzar un dado $n$ veces. Queremos calcular la probabilidad de que salgan -exactamente- $k$ veces el número tres en estos $n$ lanzamientos.\n",
    "\n",
    "* El espacio de resultados o espacio muestral $S$ lo podemos representar como un conjunto de $n$ elementos: $\\{l_1,l_2,\\dots,l_n\\}$ con $l_i$ lanzamiento $i$, por lo que se tienen $6^n$ posibilidades.\n",
    "\n",
    "* Si queremos que salgan $k$ tres, éstos pueden aparecer distribuidos de diferentes formas en los $n$ lanzamientos. Como no nos interesa el orden existen $\\binom{n}{k}$ formas posibles de realizar esto. Por ejemplo, si $k = 2$ y $n = 4$ los dos números tres pueden aparecer en los siguientes subconjuntos de lanzamientos: $\\{l_1, l_2\\}, \\{l_1, l_3\\}, \\{l_1, l_4\\}, \\{l_2, l_3\\}, \\{l_2, l_4\\} y \\{l_3, l_4\\}$.\n",
    "\n",
    "* Una vez elegidos los tres, en los otros lanzamientos pueden aparecer cualquiera de los $5$ números restantes, por lo que tenemos $5^{n-k}$ posibilidades. En resúmen, hay $\\binom{n}{k}5^{n-k}$ diferentes formas de obtener $k$ tres en $n$ lanzamientos de un dado.\n",
    "\n",
    "* Si $E=${obtener $k$ tres en $n$ lanzamientos} entonces: $$P(E) = \\frac{\\binom{n}{k}5^{n-k}}{6^n} = \\binom{n}{k}\\frac{1}{6}^k\\frac{5^{n-k}}{6^{n-k}}=\\binom{n}{k}\\left(\\frac{1}{6}\\right)^k\\left(\\frac{5}{6}\\right)^{n-k},$$ y la última igualdad es básicamente: $\\binom{n}{k}P(\\{\\text{obtener tres en k lanzamientos}\\})P(\\{\\text{no obtener tres en k lanzamientos}\\})$.\n",
    "\n",
    "* Se interpreta el evento: \"obtener un tres\", como el éxito y a \"no obtener un tres\" como el fracaso. Los lanzamientos son los ensayos del experimento binomial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Su distribución de probabilidad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En resúmen: sea $X$ la variable aleatoria asociada a un experimento binomial y $p$ la probabilidad de éxito, entonces, si $E$ representa el evento \"éxito\" y $F$ representa el evento fracaso\" la probabilidad de observar $k$ éxitos en $n$ ensayos es: $$P(X=k) = \\binom{n}{k}P(E)^{k}P(F)^{n-k}=\\binom{n}{k}p^k(1-p)^{n-k}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Comentarios**\n",
    "\n",
    "* La distribución anterior se conoce con el nombre de **distribución binomial**. \n",
    "\n",
    "* Si representamos a los éxitos y fracasos, respectivamente por los números $1$ y $0$ entonces, la variable binomial consiste en contar el número de éxitos en los $n$ ensayos.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propiedades"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* La media y la varianza de la distribición binomial con parámetros $n$ y $p$ están dadas por:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\mu = np.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sigma^2 = np(1-p).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Dado un número $n$ de ensayos, la varianza tomará su valor máximo cuando el producto $p(1-p)$ sea máximo y esto sucede para $p = \\frac{1}{2}$. Esto nos dice que: **la máxima dispersión en una distribución binomial ocurre cuando** $p=\\frac{1}{2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Su gráfica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "n_rbinom <- 500  #number of values\n",
    "n<-10 #number of trials\n",
    "p1<-0.5; p2<-0.2; p3<-0.8 #different probabilities of success\n",
    "rbinom_values1 <- rbinom(n_rbinom, n, p1)\n",
    "rbinom_values2 <- rbinom(n_rbinom, n, p2)\n",
    "rbinom_values3 <- rbinom(n_rbinom, n, p3)\n",
    "\n",
    "gf1<-ggplot(data.frame(valores=rbinom_values1,probabilidad=p1),aes(x=rbinom_values1, y=..density..))\n",
    "gf2<-ggplot(data.frame(valores=rbinom_values2,probabilidad=p2),aes(x=rbinom_values2, y=..density..))\n",
    "gf3<-ggplot(data.frame(valores=rbinom_values3,probabilidad=p3),aes(x=rbinom_values3, y=..density..))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lYOYqUDYinaJZ3EDTMbUi/pNE2h699K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\nAWIBKfw/oCgSvp/sYlEAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf1 + geom_histogram(bins = 10) + \n",
    "ggtitle('Binomial, n=10, p=0.5') +\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('rbinom')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Obsérvese que es simétrica la distribución en este caso.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PaWi/shFsTKUKzaCjGpxXptvM3+ELp+\n2bLwr5+vtivUTRXiHYgFsTIUK7TJmlq9d81d0dtmdonIsfoVNz/xt3Ub35l3vRDT46qrjQhi\nGUUnVvKNfjGxYjf6/aIgbvSDWDy5vjX53tHDK2etNxPF2vHCT743YtjICY/9K6Gy2oggllGE\nYmWE2ogglgGxIJbDGCAWxIJYUiBWKhALYkmAWAbEglgOY4BYEAtiSYFYqUAsiCUBYhkQC2I5\njAFiQSyIJQVipQKxIJYEiGVALIjlMAaIBbEglhSIlQrEglgSIJYBsSCWwxggFsSCWFIgVioQ\nC2JJgFgGxIJYDmOAWBALYkmBWKlALIglAWIZEAtiOYwBYkEsiCUFYqUCsSCWBIhlQCyI5TAG\niAWxIJYUiJUKxIJYEiCWAbEglsMYIBbEglhSIFYqEAtiSYBYBsSCWA5jgFgQC2JJgVipQCyI\nJQFiGRALYjmMAWJBLIglBWKlArEglgSIZUAsiOUwBogFsSCWFIiVCsSCWBIglgGxIJbDGCAW\nxIJYUiBWKhALYkmAWAbEglgOY4BYEAtiSYFYqUAsiCUBYhkQC2I5jAFiQSyIJQVipQKxIJYE\niGVArPQcVaLZbFBbMEYbV8GzWOwYGj0OoVUxeDEaWjw20GQqjiEHYtUq0WjWqS0Yo42r4Fks\ndgxHPQ6hRTF4MY40e2ygwaxXWu5wDsRS2wZjV2hgVwixHMYAsSAWxJICsVKBWBBLAsQyIBbE\nchgDxIJYEEsKxEoFYkEsCRDLgFgQy2EMEAtiQSwpECsViAWxJEAsA2JBLIcxQCyIBbGkQKxU\nIBbEkgCxDIgFsRzGALEgFsSSArFSgVgQSwLEMiAWxHIYA8QqRLE8ewGxeCAWxJIBsVKAWAbE\nglgOY4BYEAtiSYFYEEsGxEoBYhkQC2I5jAFiQSyIJQViQSwZECsFiGVALIjlMAaIBbEglhSI\nBbFkQKwUIJYBsSCWwxggFsSCWFIgFsSSAbFSgFgGxIJYDmOAWBALYkmBWBBLBsRKAWIZEAti\nOYwBYkEsiCUFYkEsGRArBYhlQCyI5TAGiAWxIJYUiAWxZECsFCCWAbGKVSzPcEGAWBBLCS4I\nEAtiKcEFAWJBLCW4IEAsiKUEFwSIBbGU4IIAsSCWElwQik6s6pmVw8fM2pA8edPTU0cNGzHx\nqf0Qyx1cEIpNrLkiTPnTiZPvFDbXvAWxXMEFocjEWiTElOq9qycJsSRh+khxy7zl65feJ8TQ\ntRDLDVwQikus2goxodl6bRwvRh2NnzFzXeR1WbmYALHcwAWhuMSyNlgRg1YKsVhaY4YQByGW\nC7ggFJdYd4vRkULrCDFDWuMZIbZDLBdwQSgusUaImXZpuqiU1vitEAbEcgEXhKISq0aIJ+zi\nbCHqJDVavytujHurNiKIZRSZWB8JsdAuzhdij6TG80K8CLHcwAWhqMTaJMRLdnFBwrFUrMIV\nYmJLpPhaVVXVnKNKNJsNTA2/rcgCXBBaTbXgxWho8dhAk9motmD2xdozWozcbZenlZWVfd1t\nw5nitxVZQFdo/Kc1VsrWrnD/WFGxOfpmy4oVK1YfVKLBPMzU8NuKLMAFocVUC16Mw80eG6g3\n65SWq81crPQH7zW3iKs2Jk5S27njGMsosmOstJcbDo0XV6xJmqY2IohlFJtYsQukbSkXSGtv\nF8NWJNdXGxHEMopNrEVCRG6YWZX8kU7dBDH07ZT6aiOCWEaxiVVbISaFLic03mZ/CF2/bNnW\n8OtkUf5Gan21EUEso9jECm2yplbvXXNX9LaZXUI8Yr20/VCIqg9sjkAsF3BBKDKxkm/0s8Wq\nF3GshFgu4IJQbGKZ1feOHl45a70JsbzBBaHoxMoItRFBLANiQSxFuCBALIilBBcEiAWxlOCC\nALEglhJcECAWxFKCCwLEglhKcEGAWBBLCS4IEAtiKcEFAWJBLCW4IEAsiKUEFwSIBbGU4IIQ\nQLG++NghiKUdLggBFIuo6/V/bYNYeuGCEECx/quEiAbc+zHE0gkXhACKZW770emWWh0uX9AE\nsbTBBSGIYplm25Jru1hunThxY8osiJUduCAEUyyLmkcvsNSiLz1eK5sLsbzCBSGwYlmsn3Ci\npVb3Me9CrOzDBSHIYjU8+zUKc8k6iJVtuCAEV6w1t33CcuqUH8wYQNR1FcTKMlwQAirWgarz\nQieG//1Ci3Uk//xpdCnEyjJcEIIoVuur15RaWp350532hLepN8TKMlwQAijWtP6WVaUVS9ov\nvteT4seJaiOCWEYgxbK0GvhAwm/itPTrB7GyDBeEAIrV/TvL1TSCWBnABSGAYnm5Igqx3MIF\nIYBiDRLt5ZZBgyCWFrggBFAsGtBeblY9bIdYDFwQAi9WCcTSAheEgIu1l3pALC1wQQi2WA0/\noHMhlha4IARMrH4W1KGfzUkdiX4AsbTABSFgYlEyQzxdfFAbEcQyAifWFAvqNcXmfx76uxet\nIFYauCAETKzw2wFmtlAbEcQyAinWq29BLP1wQQigWFlEbUQQy4BYEEsRLgjBEqtv3751oT/x\nQCwtcEEIllhEdDj5kgPE0gIXhGCJNWPGjKbQn3gglha4IARLrGyjNiKIZUAsiKUIFwSIBbGU\n4IIQYLFqH739J+9DLE1wQQigWIsHlYdedn/SOiXs9DuIpQcuCAEU61aaHnq5lqhnB+q8GWJp\ngQtCAMUaREutv/s60kzTOI/uhFha4IIQQLFOpg+tv09Sv1bTfIHwLR09cEEIoFidqc76exON\ntf7upGMhlha4IARQrC602/o7kH5v/T1KnSCWFrggBFCsAfSqaW4n2mKVd9EpEEsLXBACKFYl\nfamm5brIfaSLqQxiaYELQgDFWlVCHY8leiBUvit8pAWxsg8XhACKZT7SiYiubbZKLafRfIil\nBS4IQRTL3PHE4yvDhQ8nTTIglha4IARSrKyhNiKIZUAsiKUIFwSIBbGU4IIQSLGaXvrRTaOu\ns4FYWuCCEESxlvTP1pcp6pVoNhuZGn5bkQW4ILQqBi9GQ6vHBprMJrUFncR6r5Sox3lDongR\nq1aJRrOOqeG3FVmAC0KLYvBiHGn22ECDWa+03GEnsa6k7k95/qXCCGrbYOwKjUDuCk+kX2dH\nK4iVBi4IARSrc/jjZ4ilFy4IARTrNNoKsbTDBSGAYo2lP0Is7XBBCKBYW3oOPAKxdMMFIYBi\nmW/0Pv+vrRBLL1wQAijWwIF9iHqeNdAGYmmBC0IAxcJjjHIBF4QAijUuEYilBS4IARQri6iN\nCGIZEAtiKcIFAWJBLCW4IARSrJY/DTu1a+jrX9sefARi6YELQhDF2jMkdDZ4ulWqO57ehVha\n4IIQQLEay6jD8PvCYpnfo2kQSwtcEAIo1qPUY7k1MSzWC/RViKUFLggBFOtiut+MivUhnQyx\ntMAFIYBi9Q7fjxUR6xB1hlha4IIQQLE6UU1MrH3UDWJpgQtCAMXqQ+/HxFpKZ0IsLXBBCKBY\n34g7xhpN10IsLXBBCKBYc+kTW2yxni6hRRBLC1wQAihW87l0wq+20umHl44qoYu8eAWxnOGC\nEECxzO1nxm7G+swuiKUHLghBFMusuaVLWKtON9V48gpiOcMFIZBimebBF++/e9Zz+71pBbHS\nwAUhoGJlCbURQSwDYkEsRbggQCyIpQQXhGCJNU0CxNICF4RgiUUSIJYWuCAES6x+EY61fOre\nt7v199h+/SCWFrggBEusCC/16vvQDut1x4N9er3sxSuI5QwXhACKtb7rgN12cecnu26EWFrg\nghBAsUbRX2LlBTQGYmmBC0IAxepP7R/k/JtOhVha4IIQQLE6U/usA1QKsbTABSGAYp1Mz8bK\nf8KXKTTBBSGAYl1Hp++wi9tPpVEQSwtcEAIo1oZO1PunG5rN5g0zelEnnBXqgQtCAMUynw39\nEGZJ+JasTs+aXlAbEcQygimWufbSkvCnOSWXrvXkFcRyhgtCIMUyzR3zfzbtZ/N3pM6AWFmC\nC0JAxcoSaiOCWAbEgliKcEGAWBBLCS4IEAtiKcEFAWJBLCW4IEAsiKUEFwSIBbGU4IIAsSCW\nElwQIBbEUoILAsRSEMvvpOYDXHogFsRSgksPxIJYSnDpgVgQSwkuPRALYinBpQdiQSwluPRA\nLIilBJeeohOrembl8DGzNiRP3rn08clXCrEZYrmES0+xiTVXhCl/OnHykchkiOUaLj1FJtYi\nIaZU7109SYglyWJd/5PpECuXMPktKLFqK8SEZuu1cbwYdTR+RvM7hmm+BrFyCZPfghLL2mCt\nCxdWCrE4ZS7EyilMfgtKrLvF6EihdYSYAbH8hclvQYk1Qsy0S9NFJcTyFya/hSRWjRBP2MXZ\nQtRBLF9h8ltIYn0kxEK7OF+IPRDLV5j8FpJYm4R4yS4uEGJ7WrFeq6qqmnNUjt8pCQYOwY3S\n0MJU4GgyG9UW1CvWtLKysq87tON3SoKB26zlmtZYScuucMuKFStWH5Tjd0qCgUNwoxxuZipw\n1Jt1SsvVZi4WDt7zCeZQp5COsXC5IZ9g8ltQYsUukLbhAqnvMPktKLEWCRG5YWYVPtLxHSa/\nBSVWbYWY1GK9Nt5mfwhdv2zZVojlD0x+C0qs0CZravXeNXdFb5vZJcQj4cLHH3zwwe+FeN16\nMSBWTmDyW1hiJd/oFxPrpyLGUxArJzD5LTCxzOp7Rw+vnLXehFh+w+S30MTKCIeu/U5JMGDy\nC7GAGkx+IRZQg8kvxAJqMPmFWEANJr8QC6jB5BdiATWY/EIsoAaTX4gF1GDyC7GAGkx+IRZQ\ng8kvxAJqMPmFWEANJr8QC6jB5BdiATWY/EIsoAaTX4gF1GDyC7GAGkx+IRZQg8kvxAJqMPmF\nWEANJr8QC6jB5BdiATWY/EIsoAaTX4gF1GDyC7GAGkx+IRZQg8kvxAJqMPmFWEANJr8QC6jB\n5BdiATWY/EIsoAaTX4gF1GDyC7GAGkx+IRZQg8kvxAJqMPmFWEANJr8QC6jB5BdiATWY/EIs\noAaTX4gF1GDyC7GAGkx+IRZQg8kvxAJqMPmFWEANJr8QC6jB5BdiATWY/EIsoAaTX4gF1GDy\nC7GAGkx+IRZQg8kvxAJqMPmFWEANJr8QC6jB5BdiATWY/EIsoAaTX4gF1GDyC7GAGkx+IRZQ\ng8kvxAJqMPmFWEANJr+BFqtejt8pCQYOwY3S0MpU4Ggym9QWzIFYtXL8TkkwcAhulCPNTAWO\nBrNeabnDORDLYWPpd0qCAbNHCvSu0KFrv1MSDJj8QiygBpNfiAXUYPILsYAaTH4hFlCDyS/E\nAmow+YVYQA0mvxALqMHkF2IBNZj8QiygBpNfiAXUYPILsYAaTH4hFlCDyS/EAmow+YVYQA0m\nvxALqMHkF2IBNZj8QiygBpNfiAXUYPILsYAaTH4hFlCDyS/EAmow+YVYQA0mvxALqMHkF2IB\nNZj8QiygBpNfiAXUYPILsYAaTH4hFlCDyS/EAmow+YVYQA0mvxALqMHkF2IBn4BYQAsQC2gB\nYgEtQCygBYgFtACxgBYgFtACxAJagFhACxALaAFiAS1ALKAFiAW0ALGAFiAW0ALEAlqAWEAL\nEAtoAWIBLUAsoAWIBbQAsYAWIBbQAsQCWoBYQAsQC2ghv8Sqnlk5fMysDe5mQKx8Jq/EmivC\nlD/tagbEymfySaxFQkyp3rt6khBL3MyAWIEme2LVVogJzdZr43gx6qiLGRAr0GRPLGu7tC5c\nWCnEYhczIFagyZ5Yd4vRkULrCDHDxQyIFWiyJ9YIMdMuTReVLmZArECTNbFqhHjCLs4Woo6f\nAbECTdbE+kiIhXZxvhB7+BkQK9BkTaxNQrxkFxcIsT3tjNeqqqrmHJXjd0BAdnBIr16xppWV\nlX3dbcMgQLTGSlp2hVtWrFix+qASDeZhtQVjtHlc/rDZ6LGFhjqPDbSYHhs43OyxgXpTbQy1\nmYuVrYN3hqNmjdqCMVo9Ll9j1nts4ajaxyHtNLd5bKCgnvOepcsNDBDLKDaxYtdB25wukLa5\nuUDKALGMYhNrkRCR+2JWpX6kI5uhNiKIZRSbWLUVYlKL9dp4m/1Zc/2yZVulMyCWxwaKS6zQ\nlmlq9d41d0XvjtklxCPSGRDLYwNFJlby/XwxsTK60Y8BYhnFJ5ZZfe/o4ZWz1pvJYiXNgFge\nGyg6sTJCbUQQy4BYEEsOxIJYEiCWAbFkQCyIJQFiGRALYsmBWBBLAsQyIJYMiAWxJEAsA2JB\nLDkQC2JJgFgGxJIBsQIulhq//upGn9dg81cf8HkNzLGX+b0GC776hscW8k2sX5at83kNNpXN\n5CvpZeSX/V6DP5b9r8cWIFYyEMuEWDqAWGYQxVo05SOf12DnlIV8Jb08NM3vNVg2pdpjC/km\nFggIEAtoAWIBLeSXWI4Pks8Rm56eOmrYiIlP7fdtDSLU3yDEPT72/8+Hb7664tZfvtmm3kRe\nieX4IPkccaewueYtn9bA5jfCT7GafhWNQ6N6I/kkluOD5HPFSHHLvOXrl94nxNC1/qxBhA/K\nR13tn1it9wgx4aXq1a/88upgiOX4IPmcMdO+hrasXEzwZQUitIwXS0f6J9YCIZ6M7AMbg7Er\ndHyQfO6ZIcRB/3qfL+42/RPr8FViehaaySOxHB8kn3ueSXgYZo75vyuu3OWjWNb/9/tZaCaP\nxHJ8slvu+a0Qhl99t00Rz5g+ivUjMcb621DvsZn8EcvxWZS5p/W74kbfOn9Z3Nrsp1gjxcym\n+TcKMfIX27w0kz9iOT49N/c8L8SLfvW9vyL8GDvfxKoXompC5GLDMC8n5/kjluPzvnO/JleI\niS1+dT5DPBR68U0sQ4jhYtqmxtolI8VQDwdbECuFPaPFyN1+df62uC78SGvfxNpnbaomh/+t\nNg8TP1RvJ3/Eypdd4f6xomKzX50fvl5E7gn2TaxaS6zVkeJMUX5EuZ38EStPDt5rbhFX+Xfb\n/W+iGwnfxGodJoR9Rvi8lwsP+SNWflxuODReXLHGr85N8x4Rz3N+rMI4McwuvS7Ee8rN5JFY\njg+SzyG1t4thK3zqO0QeiPWr2O5ioRD/Um4mj8RyfJB87qibIIa+7U/XEfZstRkhpm7d6svH\nSiuEeCdS+rEY3qDcTB6J5fC8+BxSP1mUe/0+XZbw7wJpy83itrBP1eXi5+rN5JFYDs+Lzx1t\nPxSi6gMb9fOhrODj3Q2ry7XhnpIAAANmSURBVMUd7+796LmrRMUu9VbySSy/b/Srjz++WenP\nOkTxUSxz8RWREFzn5VbevBJL+rz43AGxbHY8MvbKa+54upav6Ux+iQUCA8QCWoBYQAsQC2gB\nYgEtQCygBYgFtACxgBYgFtACxAJagFgZM44GJk6YQX39WZN8BmJlDMRyA8TKGIjlBoiVMSli\nNR329Xvb+QnEypgUsYAEiOWOkE3v33RmafdI8b2R/Tr3/4799UN7VxiavuWm0zr3uTL23RZj\n2nk9S88YvbK9jY2V/bsMmPxv02ysuqDnsV/x6QlzOQBiucOS4sVuRNQ1XPxTZwrR9dXwvHax\n3uwZnl5q+7K0V/gtldwdbeOVbuEJn6+puShcOOYZf4ajH4jljnHU57gzHluzZk6oeHz3gS8f\n3Pe7PtRta2heTKw+vT/7hy2bH+5G/ZtCEzZ1p94Pb9/38iCih+wKvc7/y7Z144kmV3SZvnb7\nc/2o9yH/xqQViOWOcUSf3h8rnhn++bQNXeia0GtMLDovfDfvk0Thp1BcTqXhnWLtOdTtQKTC\n4PDXj4ZTx5LwT4osJ/p9ToeROyCWOywp/txefCpSuoM61ZjxYv01PLmpB/3Ievm4hO6M1FtM\nVBWpsCz8/s9E9reNz6Bbc7P+OQdiuWMcdayPFUvsrxm8RfSaGSdWz9bI9PPoJuvvM0TLI+/b\njqerIxUiT4tdS/SbyJxLaXhOVj/3QCx3jKMz2ov97ZIRESQm1ln29CE0yvo7iyj6VeaL6Yvx\nFTYT2Q92G0rf1L3mPgGx3BF38WocnW2X6onuNxMuN0QYQtdZf6cRRR/f9u3wIrEKlliR80lL\nrG/oXnOfgFjuSBDrVLuUvMVKFCtui3WJvcWCWCCJBLGcjrESxYo7xjrRPsaCWCCJBLHIfgbA\nhKSzwkSxrLNC+/ct3oyeFUIskESiWANCPpn/7Jp0HStRLOvIqkv4J3nqzotex4JYIIkEsY7v\ndu6rh4wn+yZfeU8Sa1N3Ov43O/+9+ILYlXeIBZJIEGvgnzpFPit8JTzBSSzzzehnhdMS24BY\nIEqiWOaqa07p3G9M6t0NEaJimft+OOjY0tOvX5nUBsQCQBGIBbQAsYAWIBbQAsQCWoBYQAsQ\nC2gBYgEtQCygBYgFtACxgBYgFtACxAJagFhAC/8PHliT+Rpc6s8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf2 + geom_histogram(bins = 7) + \n",
    "ggtitle('Binomial, n=10, p=0.2') +\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('rbinom')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Obsérvese que está sesgada a la derecha la distribución en este caso.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JiNAWtorg9YgSkaQ3CxBA1EzKBjiPp8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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf3 + geom_histogram(bins = 7) + \n",
    "ggtitle('Binomial, n=10, p=0.8') +\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('rbinom')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Obsérvese que está sesgada a la izquierda la distribución en este caso.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) La probabilidad de obtener $4$ veces el número tres en $10$ lanzamientos de un dado se calcula poniendo: $n = 10,k = 4$ y $p = \\frac{1}{6}$ para obtener: $$P(X=4) = \\binom{10}{4}\\left(\\frac{1}{6}\\right)^4\\left(\\frac{5}{6}\\right)^{10-4} \\approx 0.0543.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**en R...**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0542658758509881"
      ],
      "text/latex": [
       "0.0542658758509881"
      ],
      "text/markdown": [
       "0.0542658758509881"
      ],
      "text/plain": [
       "[1] 0.05426588"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(4,10,1/6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El número medio de tres que se obtienen en $10$ lanzamientos es de:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\mu = np = 10*\\frac{1}{6} = \\frac{5}{3} \\approx 1.67.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "con desviación estándar:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sigma = \\sqrt{np(1-p)} = \\sqrt{10*\\frac{1}{6}*\\frac{5}{6}} \\approx 1.18.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) La probabilidad de que los $5$ pacientes tratados con el medicamento desarrollen hipertensión arterial se calcula poniendo: $n = 5, k = 5$ y $p = 0.1$ para obtener: $$P(X=5)=\\binom{5}{5}(0.1)^5(0.9)^0 \\approx .00001.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**en R ...**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1e-05"
      ],
      "text/latex": [
       "1e-05"
      ],
      "text/markdown": [
       "1e-05"
      ],
      "text/plain": [
       "[1] 1e-05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(5,5,.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El número medio de pacientes que desarrollan hipertensión arterial es de: $$ \\mu=np=5*0.1=.5$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "con desviación estándar: $$\\sigma=\\sqrt{np(1-p)} = \\sqrt{5*0.1*0.9} \\approx 0.67$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Igual que el ejemplo $1$ pero ahora se utiliza $Y = \\frac{X}{n}$, entonces $Y$ mide la **proporción** de números tres en $n=10$ lanzamientos de un dado. Por las propiedades de media y desviación estándar se tiene:\n",
    "\n",
    "* El número medio de la proporción de tres que se obtienen en $10$ lanzamientos es de: $$\\mu_Y = \\frac{\\mu_X}{n} = \\frac{np}{n} = p = \\frac{1}{6}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* La desviación estándar de la proporción de tres que se obtienen en $10$ lanzamientos es de: $$\\sigma_Y = \\frac{\\sigma_X}{n} = \\frac{\\sqrt{np(1-p)}}{n} = \\sqrt{\\frac{np(1-p)}{n^2}} = \\sqrt{\\frac{p(1-p)}{n}} \\approx \\frac{1.18}{10}\\approx .118$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Observación** \n",
    "\n",
    "Como $\\mu_Y = p$, entonces $Y$ (proporción) se nombra estimador insesgado (en promedio no sobreestiman ni subestiman a $p$).\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comentario** \n",
    "\n",
    "* Un experimento binomial puede representarse por la siguiente urna con canicas: en la urna colocamos $r$ canicas rojas y $a$ azules. El experimento consiste en extraer repetidamente canicas de la urna, con remplazo, de manera que la urna siempre contiene las mismas canicas. Si al extraer una canica al azar, ésta es roja, entonces se contabiliza como un éxito. La probabilidad de éxito está dada por la **proporción de canicas rojas**, es decir: $$p=\\frac{r}{r+a}.$$\n",
    "\n",
    "    Supongamos que no sabemos de antemano la proporción de canicas de cada color, por lo tanto desconocemos $p$. Para tratar de averiguar esta proporción empezamos a extraer canicas con remplazo. Sea $n$ el número de veces que repetimos este proceso de extracción y $k$ el número de canicas rojas o éxitos que obtenemos. *Jacobo Bernoulli* se dio cuenta de que si $n$ era suficientemente grande, entonces la proporción $\\frac{k}{n}$ se parecía cada vez más a la probabilidad p, es decir, a la proporción real de canicas. La prueba formal de este hecho, que nos puede parecer trivial, es uno de los grandes teoremas de la Estadística por su importancia para la inferencia y se conoce como el **Teorema de Bernoulli o la Ley de los Grandes Números**.\n",
    "    \n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Normal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Un poco de historia...**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El matemático y estadístico francés Abraham de Moivre (1667 - 1754) notó que cuando la distribución binomial involucraba un gran número de ensayos (por ejemplo la probabilidad de obtener al menos $60$ caras iguales al lanzar una moneda $100$ veces), su forma podía reproducirse con una curva suave en forma de campana."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Asro3HUCv+WwKsbpkBSrtrqHJZtYfWC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\nE5FwWDwRyf8DiZcZnq6YsVUAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(2000)\n",
    "vec <- seq(-3,3,by=.1) \n",
    "dnorm_values <- dnorm(vec)  #evaluate dnorm in vec\n",
    "qplot(vec,dnorm_values,geom='line') +  #qplot is quickplot\n",
    "ggtitle('Normal estandar') + \n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('vec')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "n_rbinom<-1000 #number of values\n",
    "n1<-60 #number of trials\n",
    "p<-1/2 #probability of success\n",
    "rbinom_values1 <- rbinom(n_rbinom,n1,p)\n",
    "dbinom_values1 <- dbinom(rbinom_values1,n1,p) #evaluate dbinom in rbinom_values1\n",
    "\n",
    "#Increasing number of trials\n",
    "n2<-100\n",
    "rbinom_values2 <- rbinom(n_rbinom,n2,p)\n",
    "dbinom_values2 <- dbinom(rbinom_values2,n2,p)\n",
    "gf1 <- ggplot(data.frame(x=rbinom_values1,y=dbinom_values1),aes(x=rbinom_values1,y=..density..))\n",
    "gf2 <- ggplot(data.frame(x=rbinom_values2,y=dbinom_values2),aes(x=rbinom_values2,y=..density..))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = \"cs\")'\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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2+8seHxx+0dfcQA/Bz7RPj++++vX7/e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yMj6fv3r16mHDhnWyM3PydPPmzbabaJou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\nCAEAwKf9f4WV2UekAlMVAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf1 + geom_histogram(bins=9)+\n",
    "ggtitle('n=60,p=.5') + \n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('rbinom') + \n",
    "geom_smooth(aes(x=rbinom_values1,y=dbinom_values1), colour='red', size=.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = \"cs\")'\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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AgBnBpnNo8rLtYoFLnSftxE9zhOv3Ah09DAHzxIOwpIEAohgFMbWVHhpdMd69/f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\nq/0/JXdxz6PXFO4AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf2 + geom_histogram(bins=10)+\n",
    "ggtitle('n=100,p=.5') + \n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('rbinom') + \n",
    "geom_smooth(aes(x=rbinom_values2,y=dbinom_values2), colour='red', size=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y encontró una fórmula para aproximar las probabilidades binomiales cuando se tenía un gran número de ensayos. Esta curva fue descubierta en forma independiente por Pierre S. Laplace (1749 - 1827), en 1778 y por el alemán Carl F. Gauss en 1809. Hoy en día también es conocida como la distribución Gaussiana o campana de Gauss. Entre otras aportaciones, Gauss observó y estudió que los errores en mediciones suelen seguir una distribución normal y los errores pequeños (que producen subestimación de la cantidad real medida) ocurren con mayor frecuencia que los grandes (que producen sobrestimación)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Comentario** \n",
    "\n",
    "Otros datos que típicamente están distribuidos normal: las calificaciones de un grupo de estudiantes, el rendimiento de una vaca lechera, la altura de los individuos de una población, el nivel de consumo de un producto, el tiempo dedicado para tomar ciertas decisiones...\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Su función de densidad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Está en términos de su $\\mu$ y su $\\sigma$ y es: $$f(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}}exp\\left(-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^2\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La media $\\mu$ da el centro de la curva. La desviación estándar $\\sigma$, determina el ancho de la misma."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La distribución normal estándar es aquella en la que $\\mu = 0 , \\sigma = 1$: $$f(x) = \\frac{1}{\\sqrt{2\\pi}}exp\\left(-\\frac{x^2}{2}\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "vec <- seq(-5,8,by=.1) #number of values\n",
    "dnorm_values1 <- dnorm(vec) #evaluate density in vec\n",
    "dnorm_values2 <- dnorm(vec,1,1)\n",
    "dnorm_values3 <- dnorm(vec,1,2) #mean 1 and standar deviation of 2\n",
    "\n",
    "df1 <- data.frame(values=dnorm_values1,normal=rep('estandar',NROW(dnorm_values1)))\n",
    "df2 <- data.frame(values=dnorm_values2,normal=rep('media y desv_est 1',NROW(dnorm_values2)))\n",
    "df3 <- data.frame(values=dnorm_values3,normal=rep('media 1 y desv_est 2',NROW(dnorm_values3)))\n",
    "df <- rbind(df1,df2,df3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>values</th><th scope=col>normal</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1.486720e-06</td><td>estandar</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2.438961e-06</td><td>estandar</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>3.961299e-06</td><td>estandar</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>6.369825e-06</td><td>estandar</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1.014085e-05</td><td>estandar</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>1.598374e-05</td><td>estandar</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & values & normal\\\\\n",
       "  & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 & 1.486720e-06 & estandar\\\\\n",
       "\t2 & 2.438961e-06 & estandar\\\\\n",
       "\t3 & 3.961299e-06 & estandar\\\\\n",
       "\t4 & 6.369825e-06 & estandar\\\\\n",
       "\t5 & 1.014085e-05 & estandar\\\\\n",
       "\t6 & 1.598374e-05 & estandar\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | values &lt;dbl&gt; | normal &lt;chr&gt; |\n",
       "|---|---|---|\n",
       "| 1 | 1.486720e-06 | estandar |\n",
       "| 2 | 2.438961e-06 | estandar |\n",
       "| 3 | 3.961299e-06 | estandar |\n",
       "| 4 | 6.369825e-06 | estandar |\n",
       "| 5 | 1.014085e-05 | estandar |\n",
       "| 6 | 1.598374e-05 | estandar |\n",
       "\n"
      ],
      "text/plain": [
       "  values       normal  \n",
       "1 1.486720e-06 estandar\n",
       "2 2.438961e-06 estandar\n",
       "3 3.961299e-06 estandar\n",
       "4 6.369825e-06 estandar\n",
       "5 1.014085e-05 estandar\n",
       "6 1.598374e-05 estandar"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>values</th><th scope=col>normal</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>388</th><td>0.0010145240</td><td>media 1 y desv_est 2</td></tr>\n",
       "\t<tr><th scope=row>389</th><td>0.0008612845</td><td>media 1 y desv_est 2</td></tr>\n",
       "\t<tr><th scope=row>390</th><td>0.0007293654</td><td>media 1 y desv_est 2</td></tr>\n",
       "\t<tr><th scope=row>391</th><td>0.0006161096</td><td>media 1 y desv_est 2</td></tr>\n",
       "\t<tr><th scope=row>392</th><td>0.0005191406</td><td>media 1 y desv_est 2</td></tr>\n",
       "\t<tr><th scope=row>393</th><td>0.0004363413</td><td>media 1 y desv_est 2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & values & normal\\\\\n",
       "  & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t388 & 0.0010145240 & media 1 y desv\\_est 2\\\\\n",
       "\t389 & 0.0008612845 & media 1 y desv\\_est 2\\\\\n",
       "\t390 & 0.0007293654 & media 1 y desv\\_est 2\\\\\n",
       "\t391 & 0.0006161096 & media 1 y desv\\_est 2\\\\\n",
       "\t392 & 0.0005191406 & media 1 y desv\\_est 2\\\\\n",
       "\t393 & 0.0004363413 & media 1 y desv\\_est 2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | values &lt;dbl&gt; | normal &lt;chr&gt; |\n",
       "|---|---|---|\n",
       "| 388 | 0.0010145240 | media 1 y desv_est 2 |\n",
       "| 389 | 0.0008612845 | media 1 y desv_est 2 |\n",
       "| 390 | 0.0007293654 | media 1 y desv_est 2 |\n",
       "| 391 | 0.0006161096 | media 1 y desv_est 2 |\n",
       "| 392 | 0.0005191406 | media 1 y desv_est 2 |\n",
       "| 393 | 0.0004363413 | media 1 y desv_est 2 |\n",
       "\n"
      ],
      "text/plain": [
       "    values       normal              \n",
       "388 0.0010145240 media 1 y desv_est 2\n",
       "389 0.0008612845 media 1 y desv_est 2\n",
       "390 0.0007293654 media 1 y desv_est 2\n",
       "391 0.0006161096 media 1 y desv_est 2\n",
       "392 0.0005191406 media 1 y desv_est 2\n",
       "393 0.0004363413 media 1 y desv_est 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tail(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "gf<-ggplot(df,aes(x=rep(vec,3),y=values, color=normal))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=9, repr.plot.height=7) #esta línea sólo se ejecuta para jupyterlab con R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LzqUUQma54SKaWWzaiYRFKSKTXteqAiIhNUfwEAsDEEKsBI0OVpEQkKrmdUcskg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\nB57B0vHOVmyxAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 540
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_line() + xlab('') + ylab('dnorm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propiedades"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Moda, media y mediana son iguales por su simetría.\n",
    "\n",
    "* El $68\\%$ de los datos se encuentran a una distancia de $\\sigma$ de la media, el $95\\%$ a una distancia de $1.96\\sigma$ ($\\approx 2\\sigma$) y el $99\\%$ a una distancia de $2.58\\sigma$ ($\\approx 3\\sigma$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://dl.dropboxusercontent.com/s/vl73m3jds9dgsvp/normal_68_95_99.png?dl=0\" heigth=\"400\" width=\"400\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Si $X$ se distribuye normal con media $\\mu$ y desviación estándar $\\sigma$ (escrito: $X\\sim N(\\mu,\\sigma))$ entonces $$Z=\\frac{X-\\mu}{\\sigma},$$ es una variable aleatoria normal con media $0$ y desviación estándar $1$: $Z \\sim N(0,1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1)Si $X \\sim N(1,2)$ calcular: $P(1<X<5)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nuevamente usando: $$P(1 < X < 5) = 1 - P((1 < X < 5)^c) = 1 - P( (1 < X)^c \\cup (X <5)^c)=$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$1 - P( X \\leq 1 \\cup 5 \\leq X) = 1 - (P(X \\leq 1) + P( 5 \\leq X))$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.477249868051821"
      ],
      "text/latex": [
       "0.477249868051821"
      ],
      "text/markdown": [
       "0.477249868051821"
      ],
      "text/plain": [
       "[1] 0.4772499"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_value <- 1\n",
    "right_value <- 5\n",
    "mean_value <- 1\n",
    "std_dev <- 2\n",
    "1-pnorm(left_value,mean_value,std_dev)-pnorm(right_value,mean_value,std_dev, lower.tail = F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2)Si $Z \\sim N(0,1)$ calcular: $P(Z>0), P(Z<-1), P(-1<Z<0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el cálculo de $P(Z>0)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.5"
      ],
      "text/latex": [
       "0.5"
      ],
      "text/markdown": [
       "0.5"
      ],
      "text/plain": [
       "[1] 0.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_value <- 0\n",
    "pnorm(left_value,lower.tail=F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el cálculo de P(Z<-1):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por simetría de la normal se tiene: $P(Z<-1)=P(Z>1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.158655253931457"
      ],
      "text/latex": [
       "0.158655253931457"
      ],
      "text/markdown": [
       "0.158655253931457"
      ],
      "text/plain": [
       "[1] 0.1586553"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_value <- 1\n",
    "pnorm(left_value,lower.tail=F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De igual forma por simetría: $P(-1<Z<0) = P(0<Z<1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**(Tarea) Ejercicio**\n",
    "\n",
    "Calcular este caso.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Teorema del límite central"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=5, repr.plot.height=5) #esta línea sólo se ejecuta para jupyterlab con R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El hecho de que para un gran número de ensayos una distribución binomial se parezca, cada vez más a una normal, es un resultado parecido al Teorema de Bernoulli o Ley de los Grandes Números. Esencialmente es también una ley de los grandes números. La versión más general de este tipo de resultados es el llamado **Teorema del Límite Central** por el matemático ruso Aleksandr Lyapunov. En términos simples, el teorema nos dice que si tenemos **cierto número de variables aleatorias independientes con la misma distribución**, al aumentar su número, la **distribución de la suma** de sus resultados se **aproxima a una distribución normal**. Esto sucede **independientemente de cual sea la distribución original de las variables.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El resultado del teorema aplica si cambiamos la palabra suma por **media**. Podemos, por ejemplo, iniciar con una distribución uniforme, tomar muestras aleatorias de tamaño dos y calcular sus medias. Después procedemos con muestras de tamaño tres, cuatro y así sucesivamente aumentamos el tamaño de la muestra. La **distribución de estas medias se aproxima a una normal con la misma media de la distribución original**. **La varianza de esta distribución normal disminuye conforme aumentamos el tamaño de la muestra**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**Nota** \n",
    "\n",
    "El segundo momento de la distribución de la variable aleatoria que será sumada debe ser finito.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lanzamos **un dado** $100$ veces y hacemos un histograma con los resultados. Después tomamos **dos dados** y los lanzamos $50$ veces. **Sumamos** los números de las dos caras que aparecen en cada lanzamiento y realizamos un histograma con ellos. Tomamos ahora **tres dados** y lanzamos los tres juntos $50$ ocasiones. **Sumamos** los números de las tres caras que aparecen en cada lanzamiento y realizamos un histograma con los resultados. Las siguientes figuras muestran estos histogramas. Visualmente observamos como la **distribución de la suma de las caras tiende a ser normal**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Caso de **un dado**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "n_sample<-100\n",
    "prob<-rep(1/6,6)\n",
    "die <-sample(1:6,size=n_sample, replace=T,prob=prob)\n",
    "gf<-ggplot(data.frame(valores=die),aes(x=die))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NWHWFm2jpURaVO/XV1dfbXV3wRt9/E3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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_histogram(bins = 10)+\n",
    "ggtitle('Un dado') +\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Caso de **dos dados**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "n_sample<-100\n",
    "prob<-c(1,2,3,4,5,6,5,4,3,2,1)/36\n",
    "sum<-2:12\n",
    "two_dice<-sample(sum,n_sample,prob=prob,replace=T)\n",
    "gf<-ggplot(data.frame(valores=two_dice),aes(x=two_dice))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7AEhKVDWALC0iEsAWHpEJaAsHQIS0BY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\nwQnCghOEBScIC04QFpz4f5n6i7q8WSlIAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_histogram(bins = 6)+\n",
    "ggtitle('Dos dados') +\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Caso de **tres dados**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**(Tarea) Ejercicio**\n",
    "\n",
    "Calcular este caso utilizando `set.seed(2000)`, `sample`, `ggplot2`.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(Solución)** La gráfica se ve así:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAAEsCAMAAABOo35HAAACr1BMVEUAAAABAQECAgIDAwME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\nB5Ia332uk/PNAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_histogram(bins = 9)+\n",
    "ggtitle('Tres dados') +\n",
    "theme(plot.title = element_text(size=10, hjust = 0.5),\n",
    "      axis.text=element_text(size=8),\n",
    "      axis.title=element_text(size=8)) +\n",
    "xlab('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Promedios**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Caso de **dos dados**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(2000)\n",
    "n_sample <- 100\n",
    "prob <- c(1,2,3,4,5,6,5,4,3,2,1)/36\n",
    "mean_value <- (2:12)/2\n",
    "two_dice <- sample(mean_value,n_sample,prob=prob,replace=T)\n",
    "gf <- ggplot(data.frame(valores=two_dice),aes(x=two_dice))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vrl0u09c+fOvWlztKwnAukaYJndhHXpsGHDTrQ+IfKvUNtK9aXwxaVLly5fn0T3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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_histogram(bins = 6)+\n",
    "ggtitle('Promedio dos dados') +\n",
    "theme(plot.title = element_text(size=20, hjust = 0.5),\n",
    "      axis.text=element_text(size=16),\n",
    "      axis.title=element_text(size=16)) +\n",
    "xlab('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Caso de **tres dados**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**(Tarea) Ejercicio**\n",
    "\n",
    "Calcular este caso utilizando `set.seed(2000)`, `sample`, `ggplot2`.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(Solución)** La gráfica se ve así:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8mbxS+ZHvNQVrBsfqt9Lwotp2XGl5vf\nMwmyaMXVcGWFnyo46vf7Hb0PFRx+wB8e9/czr066aHrMO1kd6t9Z1kuWOYXDstg/Zk6a/6H5\nIXy7QwCyCEAWAcgiAFkEIIsAZBGALAKQRQCyCEAWAcgiAFkEIIsAZBGALAKQRQCyCEAWAcgi\nAFkEIIsAZBGALAKQRQCyCEAWAcgiAFkEIIvA/wHg5vPMUr5jzgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf + geom_histogram(bins = 9)+\n",
    "ggtitle('Promedio tres dados') +\n",
    "theme(plot.title = element_text(size=10, hjust = 0.5),\n",
    "      axis.text=element_text(size=8),\n",
    "      axis.title=element_text(size=8)) +\n",
    "xlab('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estos histogramas convergen a los de una distribución normal con media de $3.5$, igual a la de la distribución uniforme original."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distribución muestral de la media"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supongamos que tenemos una población y consideremos todas las posibles muestras de tamaño $n$ de la misma. Para cada una de estas muestras puede calcularse la media y obtenerse una distribución muestral de medias. Por el teorema del límite central, sabemos que si las muestras son suficientemente grandes, esta distribución se aproximará por una distribición normal. El siguiente resultado nos proporciona la media y la desviación estándar para esta distribución muestral."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Considérese una población cuya media es $\\mu$ y desviación estándar $\\sigma$. Las medias $\\bar{X}$ de las muestras aleatorias de tamaño $n$ siguen una distribución con media $\\mu$ y desviación estándar $\\frac{\\sigma}{\\sqrt{n}}$. Si $n$ es suficientemente grande (usualmente $n \\geq 30),$entonces, aproximadamente se tiene que, $$\\bar{X} \\sim N\\left(\\mu,\\frac{\\sigma}{\\sqrt{n}}\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto es, las medias están distribuidas normalmente y la desviación estándar de las medias de la muestra: $\\frac{\\sigma}{\\sqrt{n}}$, decrece conforme $n$ crece."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una muestra aleatoria de $36$ individuos se toma de una población cuyo ingreso mensual promedio es de $\\$25,000$ con una desviación estándar de $\\$6000$. ¿Cual es la probabilidad de que la media de la muestra esté entre $\\$23,000$ y $\\$27,000$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Buscamos: $P(23000 < \\bar{X} < 27000)$ con $\\bar{X} \\sim N\\left(25000,\\frac{6000}{\\sqrt{36}}\\right)$, entonces:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.954499736103642"
      ],
      "text/latex": [
       "0.954499736103642"
      ],
      "text/markdown": [
       "0.954499736103642"
      ],
      "text/plain": [
       "[1] 0.9544997"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_value <- 23000\n",
    "right_value <- 27000\n",
    "mu <- 25000\n",
    "sigma <- 6000/sqrt(36)\n",
    "1-pnorm(left_value, mu,sigma)-pnorm(right_value,mu,sigma,lower.tail =F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "que es consistente con el hecho que aproximadamente el $95\\%$ del área se encuentra a dos desviaciones estándar de la media:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "26960"
      ],
      "text/latex": [
       "26960"
      ],
      "text/markdown": [
       "26960"
      ],
      "text/plain": [
       "[1] 26960"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "23040"
      ],
      "text/latex": [
       "23040"
      ],
      "text/markdown": [
       "23040"
      ],
      "text/plain": [
       "[1] 23040"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu+sigma*1.96\n",
    "mu-sigma*1.96"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# (Tarea) Ejercicios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Nota: Varios de los siguientes ejercicios tienen su solución en las referencias dadas al inicio de la nota. Se sugiere resolverlos por su cuenta y posteriormente compararlos con sus respectivas soluciones.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Supóngase que el tiempo (en minutos) que una persona espera el Metrobús los días de semana sigue una distribución uniforme dada por, $$f(x) = \\begin{cases}\n",
    "\\frac{1}{12} & \\text{si } 0 \\leq x \\leq 12,\\\\\n",
    "0 & \\text{en otro caso}\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) ¿Cuál es la probabilidad que una persona espere menos de $6$ minutos?.\n",
    "\n",
    "b) ¿Su tiempo medio de espera? ¿su desviación estándar?."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) Considérese lanzamientos de una moneda no cargada. Sea $X$ la variable aleatoria que cuenta el número de águilas en $10$ lanzamientos. Calcular en *R* la probabilidad $P(X \\geq 3)$ con la función `pbinom` y `dbinom`, el número medio de águilas y su desviación estándar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Considérese una población de votantes en la ciudad de México. Se reporta que la proporción de votantes que favorecen al candidato del partido Naranja es igual a $0.40$. Dada una muestra aleatoria de $200$ votantes, ¿cuál es la probabilidad de que más de la mitad de ellos tengan intención de voto por el candidato naranja? Usar:\n",
    "\n",
    "a)`pbinom`\n",
    "\n",
    "b) El teorema del límite central y `pnorm` considerando lo que se conoce como corrección por continuidad: si $B$ es variable aleatoria binomial con $\\mu$ y $\\sigma$ entonces $P(B=k) = P(k-0.5<X<k+0.5)$ con $X$ variable aleatoria normal $N(\\mu,\\sigma)$ y $k$ un número entero no negativo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4) Supongamos que el ingreso anual de un imigrante mexicano en los EUA se distribuye de forma normal con una media de $\\$30,000$ y una desviación estándar de $\\$10,000$ dólares. ¿Cuál es la probabilidad de que un inmigrante mexicano gane menos de $\\$20,000$ dólares anuales? ¿Cuál es la probabilidad de que su ingreso sea mayor a los $\\$50,000$ dólares anuales? (usar *R*)."
   ]
  }
 ],
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