Soluciones/Práctica2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "06fa73cd-5c4d-4727-bf84-bd71bd95b6e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "library('glue')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96865dda-fa93-410c-9df6-c6066e02ea2c",
   "metadata": {},
   "source": [
    "# Práctica 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bfc9552-a3c4-41e5-94cc-5ffad64276df",
   "metadata": {},
   "source": [
    "## Ejercicio 1\n",
    "\n",
    "De un lote que contiene 15 artículos, de los cuales 4 son defectuosos, se eligen 3 artículos al azar con reposición. Si llamamos $X$ al número de artículos defectuosos entre los seleccionados:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4af98573-7916-4b74-84cd-d425e557a8d3",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Hallar la función de probabilidad puntual asociada a $X$ y graficarla usando R.\n",
    "\n",
    "Sea $S = \\{ (p_1, p_2, p_3) \\mid p_i \\in \\{D_1, \\dots, D_4, F_1, \\dots, F_{11}\\} \\}$ el espacio muestral de elegir 3 artículos con reposición de un total de 15 artículos, con 4 defectuosos ($D_i$) y 11 funcionales ($F_i$).\n",
    "\n",
    "$\\#S = 15^3 = 3375$\n",
    "\n",
    "Sea $R_X = \\{0,1,2,3\\}$ el rango de $X$ (el conjunto de posibles valores de la v.a. discreta $X$).\n",
    "\n",
    "La probabilidad puntual para un valor de $x \\in R_X$ es: $p_X(x) = P(X = x) = P(\\{ w \\in S \\mid X(w) = x \\})$\n",
    "\n",
    "Ahora calculemos $p_X$ para cada $x \\in R_X$:\n",
    "\n",
    "$p_X(0) = P(X = 0) = \\left( \\frac{11}{15} \\right)^3 \\approx 0.394370$\n",
    "\n",
    "$p_X(1) = P(X = 1) = {3 \\choose 1} \\frac{4}{15} \\left( \\frac{11}{15} \\right)^2 \\approx 0.4302$\n",
    "\n",
    "$p_X(2) = P(X = 2) = {3 \\choose 2} \\left( \\frac{4}{15} \\right)^2 \\frac{11}{15} \\approx 0.1564$\n",
    "\n",
    "$p_X(3) = P(X = 3) = \\left( \\frac{4}{15} \\right)^3 \\approx 0.01896$\n",
    "\n",
    "Para cualquier valor posible $x$ de la v.a. $X$, $p_X(x)$ se calcula tomando el combinatorio $3 \\choose x$ (en cuántas de las 3 elecciones de artículos puede haber un artículo defectuoso), multiplicado por la probabilidad de elegir $x$ artículos defectuosos: $\\left( \\frac{4}{15} \\right)^x$, y finalmente multiplicado por la probabilidad de elegir $3-x$ artículos funcionales: $\\left( \\frac{11}{15} \\right)^{3-x}$.\n",
    "\n",
    "$p_X(x) = {3 \\choose x} \\left( \\frac{4}{15} \\right)^x \\left( \\frac{11}{15} \\right)^{3-x}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "071666cb-5512-4cb1-bc48-edd6f7808b83",
   "metadata": {},
   "outputs": [],
   "source": [
    "R_X = 0:3\n",
    "p_X = function(x) choose(3,x) * (4/15)^x * (11/15)^(3-x)\n",
    "P = sapply(R_X, p_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "314c2a53-f8fb-4ecb-8701-136a09b93985",
   "metadata": {},
   "source": [
    "Veamos si coinciden los valores calculados previamente con la fórmula encontrada:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5e4dc677-b8f5-491e-9d94-e9037fb27e36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0.39437037037037</li><li>0.430222222222222</li><li>0.156444444444444</li><li>0.018962962962963</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.39437037037037\n",
       "\\item 0.430222222222222\n",
       "\\item 0.156444444444444\n",
       "\\item 0.018962962962963\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.39437037037037\n",
       "2. 0.430222222222222\n",
       "3. 0.156444444444444\n",
       "4. 0.018962962962963\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.39437037 0.43022222 0.15644444 0.01896296"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b7cfc595-c3b0-4fcf-a67d-fac858a0cfc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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AABAqsLnJWu186664pOFTIXJZ9I3p3M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\nGDBgwIABAwYeAwEJhyRftbZQMQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Probabilidad puntual”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "barplot(P, main='Probabilidad puntual', xlab='x', ylab='p_X(x)', names.arg=R_X, col='lightblue')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fadc8503-4ca9-4e25-9312-6ea660ae718c",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "¿Cuál es la probabilidad de que al menos 2 artículos sean defectuosos?\n",
    "\n",
    "$P(X \\geq 2) = p_X(2) + P_X(3)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "72b8537a-49e0-4472-926f-b7bd185355e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.175407407407407"
      ],
      "text/latex": [
       "0.175407407407407"
      ],
      "text/markdown": [
       "0.175407407407407"
      ],
      "text/plain": [
       "[1] 0.1754074"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_X(2) + p_X(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4892c47c-022b-405e-81fb-6ba4a37dfb30",
   "metadata": {},
   "source": [
    "Otra forma:\n",
    "\n",
    "$P(X \\geq 2) = 1 - P(X < 2) = 1 - (p_X(0) + p_X(1))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "386354b7-22ee-4042-9702-273e8028b87a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.175407407407408"
      ],
      "text/latex": [
       "0.175407407407408"
      ],
      "text/markdown": [
       "0.175407407407408"
      ],
      "text/plain": [
       "[1] 0.1754074"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1 - (p_X(0) + p_X(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6511210f-2d4e-434c-b1b7-a87f2f6e329a",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Hallar la función de distribución acumulada de $X$ y graficarla usando R.\n",
    "\n",
    "$F_X(x) = P(X \\leq x) = \\sum_{y \\in R_X, y \\leq x} p_X(y)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c925d6e7-ef1c-428c-88a8-e0ac00b8d65f",
   "metadata": {},
   "outputs": [],
   "source": [
    "F_X = function(x) sum(p_X(R_X[R_X <= x]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2bf26821-efec-4060-9649-89daa36830b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UCAAAECBAgQILCbBcZeID0yg1O37T4u+fPkd5NZ2r/OspFtCBAgQIAAAQIECBAY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\nAQIE5gn8FwmeZrPrOgZoAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Distribución acumulada”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(R_X, sapply(R_X, F_X), type='s', main='Distribución acumulada', ylab='F_X')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "117aaa17-872e-4a18-a261-466304a42564",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "Estimar mediante una simulación las probabilidades calculadas en el item a)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f9d1ffc8-1564-4a37-980c-92a77014d675",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p_X(0) = 0.39224\n",
      "p_X(1) = 0.42899\n",
      "p_X(2) = 0.15996\n",
      "p_X(3) = 0.01881\n"
     ]
    }
   ],
   "source": [
    "articulos = c(rep('D', 4), rep('F', 11))\n",
    "n = 100000\n",
    "\n",
    "experimento = function(x) {\n",
    "    seleccionados = sample(articulos, size=3, replace=TRUE)\n",
    "    return = sum(seleccionados == 'D') == x\n",
    "}\n",
    "\n",
    "x = 0:3\n",
    "p = rowSums(replicate(n, experimento(x))) / n\n",
    "print(glue('p_X({x}) = {p}'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7f20d06-b821-4468-9b3f-7c1fd0e20797",
   "metadata": {},
   "source": [
    "## Ejercicio 2\n",
    "\n",
    "Sea $X$ una variable aleatoria con función de distribución:\n",
    "\n",
    "$\n",
    "F_X(x) =\n",
    "\\begin{cases}\n",
    "  0 & \\text{si } x < 1 \\\\\n",
    "  0.3 & \\text{si } 1 \\leq x < 3 \\\\\n",
    "  0.4 & \\text{si } 3 \\leq x < 6 \\\\\n",
    "  0.6 & \\text{si } 6 \\leq x < 12 \\\\\n",
    "  1 & \\text{si } 12 \\leq x\n",
    "\\end{cases}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b81984c4-15dc-472f-8373-24630d3b0493",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Hallar la función de probabilidad puntual de X.\n",
    "\n",
    "$P_X(x) = F_X(x) - F_X(x^-)$\n",
    "\n",
    "Consideramos todos los $x$ donde $F_X$ pega un salto. Esto sucede en las cotas inferiores de los intervalos de partición de $F_X$.\n",
    "\n",
    "$P_X(1) = F_X(1) - F_X(1^-) = 0.3 - 0 = 0.3$\n",
    "\n",
    "$P_X(3) = F_X(3) - F_X(3^-) = 0.4 - 0.3 = 0.1$\n",
    "\n",
    "$P_X(6) = F_X(6) - F_X(6^-) = 0.6 - 0.4 = 0.2$\n",
    "\n",
    "$P_X(12) = F_X(12) - F_X(12^-) = 1 - 0.6 = 0.4$\n",
    "\n",
    "Con esta información podemos definir $P_X$ de la siguiente forma:\n",
    "\n",
    "$\n",
    "P_X(x) =\n",
    "\\begin{cases}\n",
    "  0.3 & \\text{si } x = 1 \\\\\n",
    "  0.1 & \\text{si } x = 3 \\\\\n",
    "  0.2 & \\text{si } x = 6 \\\\\n",
    "  0.4 & \\text{si } x = 12\n",
    "\\end{cases}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cecfa5eb-00ee-489a-a9e2-4696bf763323",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Calcular de dos maneras las siguientes probabilidades:\n",
    "\n",
    "**Utilizando la función de distribución**\n",
    "\n",
    "$P(3 < X \\leq 6) = F_X(6) - F_X(3) = 0.6 - 0.4 = 0.2$\n",
    "\n",
    "$P(3 \\leq X \\leq 6) = F_X(6) - F_X(3^-) = 0.6 - 0.3 = 0.3$\n",
    "\n",
    "$P(X \\geq 4) = 1 - F_X(4^-) = 1 - 0.4 = 0.6$\n",
    "\n",
    "$P(X \\geq 6) = 1 - F_X(6^-) = 1 - 0.4 = 0.6$\n",
    "\n",
    "**Utilizando la función de probabilidad puntual**\n",
    "\n",
    "$P(3 < X \\leq 6) = P_X(6) = 0.2 = 0.2$\n",
    "\n",
    "$P(3 \\leq X \\leq 6) = P_X(3) + P_X(6) = 0.1 + 0.2 = 0.3$\n",
    "\n",
    "$P(X \\geq 4) = P_X(6) + P_X(12) = 0.2 + 0.4 = 0.6$\n",
    "\n",
    "$P(X \\geq 6) = P_X(6) + P_X(12) = 0.2 + 0.4 = 0.6$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db209ff1-891d-4cdd-a360-4bb525fd41b1",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Utilizando el comando `sample`, generar 5 realizaciones de esta variable aleatoria en R.\n",
    "\n",
    "El chiste acá es usar el parámetro `prob` del comando `sample` para pasarle un vector de probabilidades asociadas a cada valor de $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d1ef841b-43a4-4858-a5ee-ce8f05cad144",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>12</li><li>1</li><li>12</li><li>3</li><li>1</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 12\n",
       "\\item 1\n",
       "\\item 12\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 12\n",
       "2. 1\n",
       "3. 12\n",
       "4. 3\n",
       "5. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 12  1 12  3  1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = c(1, 3, 6, 12)\n",
    "p = c(0.3, 0.1, 0.2, 0.4)\n",
    "n = 5\n",
    "sample(x, n, replace=TRUE, prob=p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43f3a26c-f0c3-4c55-b924-ba786aabec2d",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "Mediante una simulación, estimar las probabilidades del item b)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "626695b1-e8b4-47ca-82c3-903f3a9b0f1e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(function(X) 3 < X & X <= 6) = 0.19927\n",
      "P(function(X) 3 <= X & X <= 6) = 0.29677\n",
      "P(function(X) X >= 4) = 0.60075\n",
      "P(function(X) X >= 6) = 0.59857\n"
     ]
    }
   ],
   "source": [
    "x = c(1, 3, 6, 12)\n",
    "p = c(0.3, 0.1, 0.2, 0.4)\n",
    "n = 100000\n",
    "\n",
    "simular = function(condición) {\n",
    "    resultados = sample(x, n, replace=TRUE, prob=p)\n",
    "    p = length(Filter(condición, resultados)) / n\n",
    "    print(glue('P({match.call()[2]}) = {p}'))\n",
    "}\n",
    "\n",
    "simular(function(X) 3 < X & X <= 6)\n",
    "simular(function(X) 3 <= X & X <= 6)\n",
    "simular(function(X) X >= 4)\n",
    "simular(function(X) X >= 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9d5ba0f-7cda-49ba-bf2f-ad8bbb4a9088",
   "metadata": {},
   "source": [
    "## Ejercicio 3\n",
    "\n",
    "Definir una función en R que, dados dos vectores $x = (x_1, \\dots, x_n)$ y $p = (p_1, \\dots, p_n)$ y un número real $t$, calcule $F_X(t)$, es decir, la probabilidad de que de la variable aleatoria discreta que toma valores $x_1, \\dots, x_n$ con probabilidades $p_1, \\dots, p_n$ respectivamente, sea menor o igual que $t$. Probarla con la variable aleatoria del ejercicio 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7b36da3a-32e6-4cfb-b435-982882beb33d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F_X(t=0) = 0\n",
      "F_X(t=1) = 0.3\n",
      "F_X(t=3) = 0.4\n",
      "F_X(t=6) = 0.6\n",
      "F_X(t=12) = 1\n"
     ]
    }
   ],
   "source": [
    "F_X = function(x, p, t) sum(p[x <= t])\n",
    "x = c(1, 3, 6, 12)\n",
    "p = c(0.3, 0.1, 0.2, 0.4)\n",
    "\n",
    "for (t in c(0, 1, 3, 6, 12)) {\n",
    "    print(glue('F_X(t={t}) = {F_X(x, p, t)}'))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ee04c50-c048-4189-975b-51bfbff11e69",
   "metadata": {},
   "source": [
    "## Ejercicio 4\n",
    "\n",
    "Si $X$ es una v.a. discreta que toma solo valores enteros, probar que para todo $k \\in \\mathbb{Z}: p_X(k) = F_X(k) - F_X(k - 1)$\n",
    "\n",
    "Esto sale directo de la definición:\n",
    "\n",
    "$p_X(k) = F_X(k) - F_X(k^-) = F_X(k) - F_X(\\lim_{h \\to 0^+} k - h)$\n",
    "\n",
    "Como $X$ toma valores en $\\mathbb{Z}$ se cumple que $x_1 < x_2 < x_3 < \\dots$ ($\\mathbb{Z}$ es un conjunto infinito numerable), entonces $F_X(\\lim_{h \\to 0^+} k - h) = F_X(k - 1)$ y por lo tanto:\n",
    "\n",
    "$p_X(k) = F_X(k) - F_X(k - 1)$ como se quería probar."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84cfec2c-81b3-4e14-9743-94872f352409",
   "metadata": {},
   "source": [
    "## Ejercicio 5\n",
    "\n",
    "Calcular la esperanza de la variable aleatoria definida en el ejercicio 1 utilizando la definición y estimarla usando una simulación. Comparar los resultados.\n",
    "\n",
    "Recordando el ejercicio 1:\n",
    "\n",
    "$R_X = \\{0,1,2,3\\}$\n",
    "\n",
    "$p_X(0) \\approx 0.394370$\n",
    "\n",
    "$p_X(1) \\approx 0.4302$\n",
    "\n",
    "$p_X(2) \\approx 0.1564$\n",
    "\n",
    "$p_X(3) \\approx 0.01896$\n",
    "\n",
    "Por la definición de $E(X)$ tenemos:\n",
    "\n",
    "$E(X) = \\sum_{x \\in R_X} x p_X(x) \\approx 0 * 0.394370 + 1 * 0.4302 + 2 * 0.1564 + 3 * 0.01896 \\approx 0.79988$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "56be1256-a192-4747-a659-4017e112921a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.79457"
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       "0.79457"
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       "[1] 0.79457"
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     "metadata": {},
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   ],
   "source": [
    "articulos = c(rep('D', 4), rep('F', 11))\n",
    "n = 100000\n",
    "\n",
    "experimento = function(x) {\n",
    "    seleccionados = sample(articulos, size=3, replace=TRUE)\n",
    "    return = sum(seleccionados == 'D') == x\n",
    "}\n",
    "\n",
    "x = 0:3\n",
    "p = rowSums(replicate(n, experimento(x))) / n\n",
    "e = sum(x * p)\n",
    "e"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aced7588-d33f-4fa7-bc97-c44fb5c16ed2",
   "metadata": {},
   "source": [
    "## Ejercicio 6\n",
    "\n",
    "Definir una función en R que, dados dos vectores $x = (x_1, \\dots, x_n)$ y $p = (p_1, \\dots, p_n)$ calcule la **esperanza** de la variable aleatoria discreta que toma valores $x_1, \\dots, x_n$ con probabilidades $p_1, \\dots, p_n$ respectivamente. Probar que funciona para la variable aleatoria $X$ del ejercicio 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0ff014c9-46c3-4e60-b243-c79ef172748c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.8"
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      "text/latex": [
       "0.8"
      ],
      "text/markdown": [
       "0.8"
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      "text/plain": [
       "[1] 0.8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_X = function(x) choose(3,x) * (4/15)^x * (11/15)^(3-x)\n",
    "x = 0:3\n",
    "p = p_X(x)\n",
    "\n",
    "calcularEsperanza = function(x, p) sum(x * p)\n",
    "calcularEsperanza(x, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "967294d9-3f34-4848-8df3-e8156304981c",
   "metadata": {},
   "source": [
    "## Ejercicio 7\n",
    "\n",
    "Definir una función en R que, dados dos vectores $x = (x_1, \\dots, x_n)$ y $p = (p_1, \\dots, p_n)$ calcule la **varianza** de la variable aleatoria discreta que toma valores $x_1, \\dots, x_n$ con probabilidades $p_1, \\dots, p_n$ respectivamente. Probar que funciona para la variable aleatoria $X$ del ejercicio 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "05912ea8-adc7-4de7-9efb-11d4880cf752",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "0.586666666666667"
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       "[1] 0.5866667"
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   ],
   "source": [
    "p_X = function(x) choose(3,x) * (4/15)^x * (11/15)^(3-x)\n",
    "x = 0:3\n",
    "p = p_X(x)\n",
    "\n",
    "# Calculado con sumatoria\n",
    "calcularVarianza1 = function(x, p) sum((x - calcularEsperanza(x, p))^2 * p)\n",
    "\n",
    "# Calculado con la fórmula V(X) = E(X^2) - E(X)^2\n",
    "calcularVarianza2 = function(x, p) calcularEsperanza(x^2, p) - calcularEsperanza(x, p)^2\n",
    "\n",
    "calcularVarianza1(x, p)\n",
    "calcularVarianza2(x, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bffb29f9-e333-4dcb-b896-9571ca86aa98",
   "metadata": {},
   "source": [
    "## Ejercicio 8\n",
    "\n",
    "Sea $X$ una v.a. con distribución Bernoulli de parámetro $p$.\n",
    "\n",
    "Por tener distribución Bernoulli, vale lo siguiente:\n",
    "\n",
    "$R_X = \\{0,1\\}$ (0 = fracaso, 1 = éxito)\n",
    "\n",
    "$p_X(0) = 1 - p$\n",
    "\n",
    "$p_X(1) = p$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92a272b4-2e5a-4b13-a2f8-508d4677d5d8",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Calcular $E(X^k)$ para $k \\in \\mathbb{N}$.\n",
    "\n",
    "$E(X^k) = \\sum_{x \\in R_X} x^k p_X(x) = 0^k * p_X(0) + 1^k * p_X(1) = 0^k * (1 - p) + 1^k * p = p$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd14c931-aa64-4b3e-b341-e7056351b4d5",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Mostrar que $V(X) = p(1−p)$.\n",
    "\n",
    "Por definición:\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "V(X)\n",
    "&= \\sum_{x \\in R_X} (x - E(X))^2 p_X(x) \\\\\n",
    "&= \\sum_{x \\in R_X} (x - p)^2 p_X(x) \\\\\n",
    "&= (0 - p)^2 * p_X(0) + (1 - p)^2 * p_X(1) \\\\\n",
    "&= p^2 * (1 - p) + (1 - p)^2 * p \\\\\n",
    "&= p^2 - p^3 + (p^2 + 1 - 2p) * p \\\\\n",
    "&= p^2 - p^3 + p^3 + p - 2p^2 \\\\\n",
    "&= p - p^2 \\\\\n",
    "&= p(1 - p)\n",
    "\\end{align*}\n",
    "$\n",
    "\n",
    "Por fórmula:\n",
    "\n",
    "$V(X) = E(X^2) - E(X)^2 = p - p^2 = p(1 - p)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a77485b-d0c3-4835-8bb6-a0b43bd713ec",
   "metadata": {},
   "source": [
    "## Ejercicio 9\n",
    "\n",
    "El 70% de las consultas de un sistema interactivo de computación requiere de acceso a bases de datos. Un sistema recibe 25 consultas independientes unas de otras.\n",
    "\n",
    "$X$ = \"cantidad de consultas que requieren acceso a bases de datos\"\n",
    "\n",
    "$X \\sim Bi(25, 0.7)$ ($X$ v.a. con distribución binomial con parámetros $n=25$, $p=0.7$)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8736611d-fd85-4a76-907d-5d770a8e623a",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Cuál es la probabilidad de que:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e802529-e9a3-43f5-8a03-79ab37a8e54a",
   "metadata": {},
   "source": [
    "**¿Exactamente 20 consultas requieran acceso a una base de datos?**\n",
    "\n",
    "Recuerdo: $p_X(x) = {n \\choose x} p^x (1-p)^{n-x}$\n",
    "\n",
    "$P(X=20) = p_X(20) = {25 \\choose 20} * 0.7^{20} * (1-0.7)^{25-20} = {25 \\choose 20} * 0.7^{20} * 0.3^5 \\approx 0.103016$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "88723c59-18b5-4412-aa43-2ed59162c4d8",
   "metadata": {},
   "outputs": [
    {
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       "[1] 0.1030165"
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     },
     "metadata": {},
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    }
   ],
   "source": [
    "dbinom(20, 25, 0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5d321c8-8d01-4bf3-8115-394b663d2f8d",
   "metadata": {},
   "source": [
    "**¿El número de consultas que requieran acceso a una base de datos esté entre 20 y 24 inclusive?**\n",
    "\n",
    "$P(20 \\leq X \\leq 24) = \\sum_{x=20}^{24} p_X(x) \\approx 0.193354$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2e621057-475a-42a0-a783-174c232d6024",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.193354335226099"
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       "0.193354335226099"
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       "[1] 0.1933543"
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     },
     "metadata": {},
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    }
   ],
   "source": [
    "sum(dbinom(20:24, 25, 0.7))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "349e05a7-c82b-4ce4-997f-7481672991ae",
   "metadata": {},
   "source": [
    "Otra forma es usando la función de distribución acumulada $F_X$:\n",
    "\n",
    "$P(20 \\leq X \\leq 24) = F_X(24) - F_X(20^-) = F_X(24) - F_X(19) \\approx 0.193354$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "26db8566-663f-4223-98d8-ac8d4f11e1ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.193354335226098"
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       "0.193354335226098"
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       "[1] 0.1933543"
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     },
     "metadata": {},
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   ],
   "source": [
    "pbinom(24, 25, 0.7) - pbinom(19, 25, 0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aca56f6b-bd4c-47f7-92ab-02f3bc0f92a6",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Calcular el valor esperado y la varianza del número de consultas que requieren acceso a una base de datos.\n",
    "\n",
    "$E(X) = np = 25 * 0.7 = 17.5$\n",
    "\n",
    "$V(X) = np(1 - p) = 25 * 0.7 * (1 - 0.7) = 25 * 0.7 * 0.3 = 5.25$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67e494f9-7db2-4c00-8800-526d25f2b4da",
   "metadata": {},
   "source": [
    "## Ejercicio 10\n",
    "\n",
    "Se tienen dos dados, uno equilibrado y el otro cargado en el cual los números 1 y 2 tienen probabilidad 1/3 y el resto 1/12. Se elige un dado al azar y se lo arroja tres veces (independientemente). Sea X el número de veces que sale 1 ó 2."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb2484a2-a34c-410b-bb98-0a93349d2822",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "¿Cuál es la distribución de $X$ condicional a que se eligió el dado cargado?\n",
    "\n",
    "$X \\sim Bi(3, \\frac{2}{3})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acd326f8-26d3-4332-a947-218552fdc421",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Hallar una expresión general para $p_X(k)$.\n",
    "\n",
    "Con el dado equilibrado $D_E$ tenemos probabilidad $\\frac{2}{6} = \\frac{1}{3}$ de que salga 1 ó 2.\n",
    "\n",
    "Con el dado cargado $D_C$ tenemos probabilidad $\\frac{2}{3}$ de que salga 1 ó 2.\n",
    "\n",
    "El dado se elige al azar, así que hay $\\frac{1}{2}$ de probabilidad de elegir uno u otro, y estos son casos disjuntos.\n",
    "\n",
    "Por el teorema de la probabilidad total vale que $P(X=k) = P(X=k|D_E)P(D_E) + P(X=k|D_C)P(D_C)$\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "p_X(k)\n",
    "&= \\left( \\frac{1}{2} {3 \\choose k} \\left( \\frac{1}{3} \\right) ^k \\left( \\frac{2}{3} \\right) ^{3-k} \\right) + \\left( \\frac{1}{2} {3 \\choose k} \\left( \\frac{2}{3} \\right) ^k \\left( \\frac{1}{3} \\right) ^{3-k} \\right) \\\\\n",
    "&= \\frac{1}{2} {3 \\choose k} \\left( \\left( \\frac{1}{3} \\right) ^k \\left( \\frac{2}{3} \\right) ^{3-k} + \\left( \\frac{2}{3} \\right) ^k \\left( \\frac{1}{3} \\right) ^{3-k} \\right)\n",
    "\\end{align*}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4577212-7ab0-4b85-a7b7-bb176b24f9e4",
   "metadata": {},
   "source": [
    "## Ejercicio 11\n",
    "\n",
    "Para verificar si se cumplen las normas establecidas para arrojar residuos al río Reconquista, un inspector visita al azar 10 de las 50 industrias establecidas a orillas de dicho río."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96c0cdd1-511f-41cd-81d4-12556a43a72a",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Si en realidad 35 industrias no cumplen con alguna de las normas, ¿cuál es la distribución del número de industrias visitadas que están en infracción? Calcular la probabilidad de que 6 de las industrias visitadas estén en infracción.\n",
    "\n",
    "Es una distribución hipergeométrica con parámetros $N=50$, $D=35$, $n=10$. El \"éxito\" en este contexto es detectar una empresa en infracción.\n",
    "\n",
    "$X \\sim H(10, 50, 35)$\n",
    "\n",
    "$p_X(x) = \\frac{{D \\choose x}{N - D \\choose n - x}}{N \\choose n}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6eeb14ba-e604-4696-ade5-267a5fea1518",
   "metadata": {},
   "outputs": [
    {
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       "[1] 0.2156886"
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   ],
   "source": [
    "x = 6\n",
    "n = 10\n",
    "N = 50\n",
    "D = 35\n",
    "p_X = function(x) (choose(D, x) * choose(N - D, n - x)) / choose(N, n)\n",
    "p_X(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "720da28f-1b9a-4b20-9ee4-c852019a2e77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.21568860999799"
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       "0.21568860999799"
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       "[1] 0.2156886"
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     "metadata": {},
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    }
   ],
   "source": [
    "# Usando la función que viene con R\n",
    "dhyper(x, D, N-D, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ffc94f9-1667-433e-9b31-c00936b62f90",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Si hay 500 industrias de las cuales 350 están en infracción, aproximar la distribución de (a) por una más simple. Calcular nuevamente la probabilidad de que 6 de las industrias visitadas estén en infracción.\n",
    "\n",
    "Se puede modelar con una distribución binomial con parámetros $n = 10$ y $p = \\frac{350}{500} = 0.7$.\n",
    "\n",
    "$Y \\sim Bi(10, 0.7)$\n",
    "\n",
    "$p_Y(y) = {n \\choose y} p^y (1-p)^{n-y}$\n",
    "\n",
    "$p_Y(6) = {10 \\choose 6} * 0.7^6 * (1-0.7)^{10-6} = 0.200120949$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b332d980-817b-46af-9dd4-9803ce9e7133",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.200120949"
      ],
      "text/latex": [
       "0.200120949"
      ],
      "text/markdown": [
       "0.200120949"
      ],
      "text/plain": [
       "[1] 0.2001209"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(6, 10, 0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e377a0a1-75f9-4fc5-94e5-be1e58f1991d",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Sea $X$ el número de fábricas que están en infracción entre las 10 visitadas. Calcular $E(X)$ y $V(X)$ para las distribuciones exacta (a) y aproximada (b).\n",
    "\n",
    "**Distribución exacta hipergeométrica X**\n",
    "\n",
    "$E(X) = n \\frac{D}{N} = 10 \\frac{35}{50} = 7$\n",
    "\n",
    "$V(X) = \\frac{N-n}{N-1} n \\frac{D}{N} \\left(1 - \\frac{D}{N}\\right) = \\frac{50-10}{50-1} 10 \\frac{35}{50} \\left(1 - \\frac{35}{50}\\right) \\approx 1.714285$\n",
    "\n",
    "**Distribución aproximada binomial Y**\n",
    "\n",
    "$E(Y) = np = 10 * 0.7 = 7$\n",
    "\n",
    "$V(Y) = np(1-p) = 10 * 0.7 (1 - 0.7) = 2.1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30296db6-f040-4d3f-9abb-4e6299a88370",
   "metadata": {},
   "source": [
    "## Ejercicio 12\n",
    "\n",
    "Una rueda de ruleta está dividida en 38 secciones, de las cuales 18 son rojas, 18 son negras y las 2 restantes son verdes. Sea $X$ el número necesario de juegos hasta obtener una sección verde en jugadas independientes.\n",
    "\n",
    "Consideramos éxito cuando se obtiene una sección verde: $P(\\text{Éxito}) = \\frac{2}{38} = \\frac{1}{19}$\n",
    "\n",
    "La v.a. $X$ tiene distribución geométrica: $X \\sim G(\\frac{1}{19})$ con parámetro $p=\\frac{1}{19}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bfb0503-de81-4118-8d09-a6d5477f408a",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "¿Cuál es la probabilidad de que sean necesarias al menos 4 jugadas?\n",
    "\n",
    "Función de probabilidad puntual: $p_X(x) = p(1-p)^{x-1}$\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "P(X \\geq 4)\n",
    "&= 1 - P(X < 4) \\\\\n",
    "&= 1 - (p_X(1) + p_X(2) + p_X(3)) \\\\\n",
    "&= 1 - \\left( \\frac{1}{19} \\left(1 - \\frac{1}{19}\\right) ^ {1-1} + \\frac{1}{19} \\left(1 - \\frac{1}{19}\\right) ^ {2-1} + \\frac{1}{19} \\left(1 - \\frac{1}{19}\\right) ^ {3-1} \\right) \\\\\n",
    "&= 1 - \\left( \\frac{1}{19} + \\frac{1}{19} \\left(1 - \\frac{1}{19}\\right) + \\frac{1}{19} \\left(1 - \\frac{1}{19}\\right) ^ {2} \\right) \\\\\n",
    "& \\approx 0.850269\n",
    "\\end{align*}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baec9cb6-7906-43dd-a706-ed097f0d8fb0",
   "metadata": {},
   "source": [
    "Las funciones de R de la distribución geométrica están definidas sutilmente distintas a nuestra definición. En vez de ser $X$ = \"número de repeticiones hasta el primer éxito\" está definida como $X$ = \"número de fracasos antes del primer éxito\".\n",
    "\n",
    "Entonces si queremos calcular $P(X=4)$, en las funciones de R tenemos que pensarlo como $P(X=3)$ (porque si en la 4ta repetición obtenemos un éxito, significa que hubieron 3 fracasos anteriormente).\n",
    "\n",
    "Ojo, esto depende cómo esté definida nuestra v.a. en el enunciado o en nuestra resolución. Si se define igual a cómo la considera R entonces no hay que hacer ninguna transformación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "965356f1-cdfe-40c9-8c62-47d017faacd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "0.850269718617874"
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       "0.850269718617874"
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       "[1] 0.8502697"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sumando las probabilidades puntuales\n",
    "1 - dgeom(0, 1/19) - dgeom(1, 1/19) - dgeom(2, 1/19)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bcb10cb9-cf53-4273-8aed-79780a87db8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.850269718617874"
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       "0.850269718617874"
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       "[1] 0.8502697"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Usando la distribución acumulada\n",
    "1 - pgeom(2, 1/19)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "074aa045-17ed-4bf9-a122-1d8a0fa19d14",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Hallar la función de distribución acumulada de la v.a. $X$.\n",
    "\n",
    "$F_X(x) = \\begin{cases}\n",
    "  0 & \\text{si } x < 1 \\\\\n",
    "  1 - (1-p)^{\\lfloor x \\rfloor} & \\text{si } x \\geq 1\n",
    "\\end{cases} = \\begin{cases}\n",
    "  0 & \\text{si } x < 1 \\\\\n",
    "  1 - \\left(\\frac{18}{19}\\right)^{\\lfloor x \\rfloor} & \\text{si } x \\geq 1\n",
    "\\end{cases}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b18c329b-59c4-4145-b5f0-dd41a92438bd",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Si fueron necesarias 7 o más jugadas, ¿cuál es la probabilidad de que se necesiten al menos 10 jugadas? Comparar con (a).\n",
    "\n",
    "La distribución geométrica tiene la propiedad de \"falta de memoria\": la probabilidad de conseguir un éxito después de $n+m$ fracasos sabiendo que ya hubieron $n$ fracasos es la misma probabilidad que conseguir un éxito después de $n+m-n = m$ fracasos. Es decir, nos \"olvidamos\" de los primeros $n$ fracasos.\n",
    "\n",
    "[Acá](https://www.ugr.es/~cdpye/CursoProbabilidad/pdf/P_T05_OlvidoGeometrica.pdf) está mejor explicado con su demostración.\n",
    "\n",
    "Utilizando la función de distribución acumulada, primero buscamos una fórmula para calcular fácilmente $P(X \\geq x)$:\n",
    "\n",
    "$P(X \\geq x) = 1 - P(X < x) = 1 - F_X(x-1) = 1 - \\left(1 - \\left(\\frac{18}{19}\\right)^{x-1}\\right) = \\left(\\frac{18}{19}\\right)^{x-1}$\n",
    "\n",
    "Luego, sin utilizar la propiedad de falta de memoria, calculemos la probabilidad que pide el enunciado:\n",
    "\n",
    "$P(X \\geq 10|X \\geq 7) = \\frac{P(X \\geq 10 \\cap X \\geq 7)}{P(X \\geq 7)} = \\frac{P(X \\geq 10)}{P(X \\geq 7)} = \\frac{\\left(\\frac{18}{19}\\right)^9}{\\left(\\frac{18}{19}\\right)^6} = \\left(\\frac{18}{19}\\right)^3 \\approx 0.850269$\n",
    "\n",
    "Utilizando la propiedad de falta de memoria:\n",
    "\n",
    "$P(X > 9|X > 6) = P(X > (9-6)) = P(X > 3) = P(X \\geq 4)$\n",
    "\n",
    "Si queremos que coincida exactamente con la fórmula de los apuntes podemos escribirlo así:\n",
    "\n",
    "Sean $n=6$, $m=3$. $P(X > n+m|X > n) = P(X > m) = P(X > 3) = P(X \\geq 4)$\n",
    "\n",
    "Observemos que $P(X \\geq 4)$ es lo que calculamos en (a)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc938c49-2651-4289-bd4c-3096b9d5935f",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "¿Cuál es la probabilidad de que sea necesario un número impar de jugadas?\n",
    "\n",
    "$I = \\{ n \\in \\mathbb{N}_0 \\mid n \\text{ impar} \\} \\subset X$\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "P(I)\n",
    "&= p_X(\\{1\\} \\cup \\{3\\} \\cup \\{5\\} \\cup \\dots \\cup \\{2k+1\\}) \\\\\n",
    "&= \\sum_{k=0}^{\\infty} p(1-p)^{2k} \\\\\n",
    "&= \\sum_{k=0}^{\\infty} \\frac{1}{19}\\left(\\frac{18}{19}\\right)^{2k} \\\\\n",
    "&= \\frac{1}{19} \\sum_{k=0}^{\\infty} \\left(\\frac{18^2}{19^2}\\right)^k \\hskip1em \\text{Es una serie geométrica que converge pues:} \\frac{18^2}{19^2} < 1 \\\\\n",
    "&= \\frac{1}{19} \\frac{1}{1 - \\frac{18^2}{19^2}} \\\\\n",
    "&= \\frac{19}{37} \\approx 0.513\n",
    "\\end{align*}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1c9844c-3078-4a4a-99ca-64a868accf3a",
   "metadata": {},
   "source": [
    "### Pregunta E\n",
    "\n",
    "Hallar $E(X)$ y $V(X)$.\n",
    "\n",
    "$E(X) = \\frac{1}{p} = \\frac{1}{\\frac{1}{19}} = 19$\n",
    "\n",
    "$V(X) = \\frac{1-p}{p^2} = \\frac{1 - \\frac{1}{19}}{\\left( \\frac{1}{19} \\right) ^2} = 342$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3d6c75e-17ef-49e4-8a6e-4b219b81c6c7",
   "metadata": {},
   "source": [
    "## Ejercicio 13\n",
    "\n",
    "Si en el ejercicio anterior se define $Y$ = número de juegos hasta obtener exactamente tres secciones verdes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca338949-f9a4-4127-b9a5-98abe29707b0",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "¿Qué distribución tiene la v.a. $Y$?\n",
    "\n",
    "Tiene una distribución binomial negativa con parámetros $r=3$, $p=\\frac{1}{19}$\n",
    "\n",
    "$Y \\sim BN(3, \\frac{1}{19})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7d5e8e9-3d63-43f3-9634-09b91444f21f",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "¿Cuál es la probabilidad de que se requieran exactamente 5 jugadas?\n",
    "\n",
    "$p_Y(y) = {y-1 \\choose r-1} p^r (1-p)^{y-r}$\n",
    "\n",
    "$P(Y=5) = p_Y(5) = {5-1 \\choose 3-1} \\left( \\frac{1}{19} \\right) ^ 3 \\left( 1 - \\frac{1}{19} \\right) ^ {5-3} \\approx 0.0007851$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0954754-a885-459a-bd33-fa70c6063517",
   "metadata": {},
   "source": [
    "Las funciones de R de la distribución binomial negativa en vez de recibir $X$ = cantidad de repeticiones totales (éxitos + fracasos) espera recibir la cantidad de fracasos (el total de repeticiones se determina sumando los fracasos + éxitos)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "450bd6dd-f3e1-4d3c-a6ec-3d0bb3cae7fc",
   "metadata": {},
   "outputs": [
    {
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       "0.000785105926701638"
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       "[1] 0.0007851059"
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   ],
   "source": [
    "y = 5 # Cantidad total de repeticiones\n",
    "r = 3 # Cantidad de éxitos\n",
    "p = 1/19 # Probabilidad de éxito\n",
    "\n",
    "dnbinom(y - r, r, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b820087-505f-4003-8837-8d9be86db48a",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Hallar $E(Y)$ y $V(Y)$.\n",
    "\n",
    "$E(Y) = \\frac{r}{p} = \\frac{3}{\\frac{1}{19}} = 57$\n",
    "\n",
    "$V(X) = \\frac{r(1-p)}{p^2} = \\frac{3\\left(1 - \\frac{1}{19}\\right)}{\\left( \\frac{1}{19} \\right) ^2} = 1026$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3c0f97c-d424-4dcd-b005-2962cb75323f",
   "metadata": {},
   "source": [
    "## Ejercicio 14\n",
    "\n",
    "Con el fin de encontrar una palabra clave, un motor de búsqueda de internet explora una secuencia de sitios de la WEB en orden aleatorio. Al iniciar la búsqueda, el motor elige, al azar y con igual probabilidad, una entre dos secuencias posibles de sitios. Se sabe que el 10% de los sitios de la primera secuencia contienen esta palabra clave, mientras que sólo el 5% de los sitios de la segunda contienen dicha palabra."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23853104-92f2-4652-a94a-962b38f491af",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Si la búsqueda termina ni bien se encuentra un sitio que contenga la palabra clave, ¿cuál es la probabilidad de que más de 5 sitios deban ser explorados?\n",
    "\n",
    "$S_i$ = \"secuencia i de sitios\"\n",
    "\n",
    "$S_i \\cap S_j = \\emptyset$ $\\forall i \\neq j$\n",
    "\n",
    "$P(S_i) = \\frac{1}{2}$ $\\forall i$\n",
    "\n",
    "$X$ = \"número de sitios que deben ser explorados hasta encontrar la palabra clave\"\n",
    "\n",
    "$X \\sim G(p)$ El parámetro $p$ depende de la secuencia en donde se está buscando.\n",
    "\n",
    "$X|S_1 \\sim G(\\frac{1}{10})$\n",
    "\n",
    "$X|S_2 \\sim G(\\frac{1}{20})$\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "P(X > 5)\n",
    "&= P((X > 5) \\cap S_1) + P((X > 5) \\cap S_2) \\\\\n",
    "&= P(X|S_1 > 5)P(S_1) + P(X|S_2 > 5)P(S_2) \\\\\n",
    "&= (1 - P(X|S_1 \\leq 5))P(S_1) + (1 - P(X|S_2 \\leq 5))P(S_2) \\\\\n",
    "&= (1 - F_{X|S_1}(5))P(S_1) + (1 - F_{X|S_2}(5))P(S_2) \\\\\n",
    "&= \\left(1 - \\left(1 - \\left(1 - \\frac{1}{10}\\right)^5\\right)\\right)\\frac{1}{2} + \\left(1 - \\left(1 - \\left(1 - \\frac{1}{20}\\right)^5\\right)\\right)\\frac{1}{2} \\\\\n",
    "&\\approx 0.682135\n",
    "\\end{align*}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ddfbd163-ea5c-45d7-bd87-9d52919c39ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "0.68213546875"
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       "[1] 0.6821355"
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   ],
   "source": [
    "(1 - pgeom(4, 1/10)) * 1/2 + (1 - pgeom(4, 1/20)) * 1/2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae064fda-3446-4d39-a95d-01a5c8c70b4c",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Si se sabe que el motor de búsqueda encontró la palabra clave en la sexta visita ¿cuál es la probabilidad de que la haya encontrado en la segunda secuencia?\n",
    "\n",
    "$P(S_2|(X = 6)) = \\frac{P(S_2 \\cap (X = 6))}{P(X = 6)} = \\frac{P(X|S_2 = 6)P(S_2)}{P(X|S_1 = 6)P(S_1) + P(X|S_2 = 6)P(S_2)} \\approx 0.395844$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "cd2abfca-c0a0-4a33-98c2-801a566c8628",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.395844280830376"
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       "0.395844280830376"
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       "0.395844280830376"
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      "text/plain": [
       "[1] 0.3958443"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(dgeom(5, 1/20) * 1/2) / (dgeom(5, 1/10) * 1/2 + dgeom(5, 1/20) * 1/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9750bdff-82a5-4274-87a1-0db1f97ff308",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Si la búsqueda termina cuando se encuentran 2 sitios que contenga la palabra clave ¿cuál es la probabilidad de que deban explorarse exactamente 10 sitios?\n",
    "\n",
    "Usemos otra distribución que modela mejor el problema.\n",
    "\n",
    "$Y$ = \"número de sitios que deben ser explorados hasta encontrar la palabra clave en exactamente $r$ sitios\"\n",
    "\n",
    "Igual que antes, el parámetro $p$ de la distribución depende de la secuencia en donde se esté buscando.\n",
    "\n",
    "$Y|S_1 \\sim BN(2, \\frac{1}{10})$\n",
    "\n",
    "$Y|S_2 \\sim BN(2, \\frac{1}{20})$\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "P(Y = 10)\n",
    "&= P((Y = 10) \\cap S_1) + P((Y = 10) \\cap S_2) \\\\\n",
    "&= P(Y|S_1 = 10)P(S_1) + P(Y|S_2 = 10)P(S_2) \\\\\n",
    "&\\approx 0.026834\n",
    "\\end{align*}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d401e3d3-3ea0-4cd7-967a-3a9e5811919b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0268345043020019"
      ],
      "text/latex": [
       "0.0268345043020019"
      ],
      "text/markdown": [
       "0.0268345043020019"
      ],
      "text/plain": [
       "[1] 0.0268345"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dnbinom(8, 2, 1/10) * 1/2 + dnbinom(8, 2, 1/20) * 1/2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7ff35b2-b0cd-418f-9698-a826d063abd5",
   "metadata": {},
   "source": [
    "## Ejercicio 15\n",
    "\n",
    "Un minorista ha verificado que la demanda semanal de cajones de cierto producto es una v.a. con distribución de Poisson de parámetro $\\lambda = 2$. Completa su existencia los lunes por la mañana de manera de tener 4 cajones al principio de la semana. Al efectuar un análisis de la actividad de su negocio, se le plantean las siguientes preguntas:\n",
    "\n",
    "$X \\sim P(2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6c20b8f-508e-41f3-9289-d944596d4ccd",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "¿Cuál es la probabilidad de vender todo su stock durante la semana?\n",
    "\n",
    "$P(X \\geq 4) = 1 - P(X \\leq 3) = 1 - F_X(3) \\approx 0.142876$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9a14f089-4984-408b-9993-204a1aa50b17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.142876539501453"
      ],
      "text/latex": [
       "0.142876539501453"
      ],
      "text/markdown": [
       "0.142876539501453"
      ],
      "text/plain": [
       "[1] 0.1428765"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1 - ppois(3, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52af450e-bd88-414f-bbed-92a9e1806152",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "¿Cuál es la probabilidad de que sea incapaz de cumplir con un pedido por lo menos?\n",
    "\n",
    "$P(X \\geq 5) = 1 - P(X \\leq 4) = 1 - F_X(4) \\approx 0.052653$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3ad78157-cbbc-44bb-a87c-de8c38f0ce45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0526530173437111"
      ],
      "text/latex": [
       "0.0526530173437111"
      ],
      "text/markdown": [
       "0.0526530173437111"
      ],
      "text/plain": [
       "[1] 0.05265302"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1 - ppois(4, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b148da17-977d-4b70-b9d0-e73ed84e004b",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "¿Cuál es la distribución del número de cajones vendidos en una semana?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a8dd0934-a1be-4910-8dfa-f84488c7e34a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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FybeFfS3l8Na99H9///Zl63LWRb6zwz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\nAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Distribución del número de cajones vendidos en una semana”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "barplot(dpois(0:4, 2), main='Distribución del número de cajones vendidos en una semana', xlab='cajones vendidos', ylab='p_X(x)', names.arg=0:4, col='lightblue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "284ab061-5124-48b2-8262-49587278c9a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 5 × 2 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0.13533528</td></tr>\n",
       "\t<tr><td>1</td><td>0.27067057</td></tr>\n",
       "\t<tr><td>2</td><td>0.27067057</td></tr>\n",
       "\t<tr><td>3</td><td>0.18044704</td></tr>\n",
       "\t<tr><td>4</td><td>0.09022352</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 5 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       "\t 0 & 0.13533528\\\\\n",
       "\t 1 & 0.27067057\\\\\n",
       "\t 2 & 0.27067057\\\\\n",
       "\t 3 & 0.18044704\\\\\n",
       "\t 4 & 0.09022352\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 5 × 2 of type dbl\n",
       "\n",
       "| 0 | 0.13533528 |\n",
       "| 1 | 0.27067057 |\n",
       "| 2 | 0.27067057 |\n",
       "| 3 | 0.18044704 |\n",
       "| 4 | 0.09022352 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]      \n",
       "[1,] 0    0.13533528\n",
       "[2,] 1    0.27067057\n",
       "[3,] 2    0.27067057\n",
       "[4,] 3    0.18044704\n",
       "[5,] 4    0.09022352"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matrix(c(0:4, dpois(0:4, 2)), nrow=5, ncol=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a99d848-80eb-4522-8a08-fe016a9aed1f",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "¿Con cuántos cajones debería iniciar la semana a fin de que la probabilidad de cumplir con todos sus pedidos fuese mayor o igual que 0.99?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "30808e1e-2c33-448f-89ff-2291a6a8efb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6"
      ],
      "text/latex": [
       "6"
      ],
      "text/markdown": [
       "6"
      ],
      "text/plain": [
       "[1] 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 0\n",
    "repeat {\n",
    "    if (ppois(x, 2) >= 0.99) break\n",
    "    x = x + 1\n",
    "}\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed64ff26-5bcd-44a9-b4ea-e3517493e817",
   "metadata": {},
   "source": [
    "## Ejercicio 16\n",
    "\n",
    "Un bibliotecario ubica 1000 libros en un cierto día. Si la probabilidad de que un libro cualquiera sea mal ubicado es 0.001 y los libros se ubican en forma independiente, ¿cuál es la distribución aproximada del número de libros mal ubicados en ese día?\n",
    "\n",
    "$X$ = \"cantidad de libros mal ubicados en un día\"\n",
    "\n",
    "La v.a. $X$ podría tener una distribución binomial con parámetros $n=1000$, $p=0.001$.\n",
    "\n",
    "Esta distribución binomial se puede aproximar con una distribución de Poisson con parámetro $\\lambda = np = 1000 * 0.001 = 1$.\n",
    "\n",
    "$X \\sim P(1)$\n",
    "\n",
    "Utilizando esta distribución, calcular la probabilidad de que:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ca3ad2b-5aa7-4934-8d70-a4d2cd6b835e",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Por lo menos un libro sea mal ubicado ese día.\n",
    "\n",
    "Recuerdo: $p_X(x) = \\frac{e^{-\\lambda}\\lambda^x}{x!}$\n",
    "\n",
    "$P(X \\geq 1) = 1 - P(X=0) = 1 - \\frac{e^{-1}1^0}{0!} = 1 - \\frac{1}{e} \\approx 0.63212$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "20c3e1d0-bcbd-4eb3-ac35-1241bdb57616",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.632120558828558"
      ],
      "text/latex": [
       "0.632120558828558"
      ],
      "text/markdown": [
       "0.632120558828558"
      ],
      "text/plain": [
       "[1] 0.6321206"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1 - dpois(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7afad0e8-41f9-477e-8a97-96fc0d57c916",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Exactamente 3 libros sean mal ubicados ese día. Comparar con el valor exacto.\n",
    "\n",
    "$P(X=3) = \\frac{e^{-1}1^3}{3!} = \\frac{1}{e3!} \\approx 0.061313$\n",
    "\n",
    "Usando la distribución binomial:\n",
    "\n",
    "$P(X=3) = {1000 \\choose 3} * 0.001^3 * (1 - 0.001)^{1000-3} \\approx 0.061282$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3bca3177-288d-4b7e-8d1d-6831d680527a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0613132401952404"
      ],
      "text/latex": [
       "0.0613132401952404"
      ],
      "text/markdown": [
       "0.0613132401952404"
      ],
      "text/plain": [
       "[1] 0.06131324"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dpois(3, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "1c86bafc-bab3-4051-b644-e30c9bad0ee9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0612825093898406"
      ],
      "text/latex": [
       "0.0612825093898406"
      ],
      "text/markdown": [
       "0.0612825093898406"
      ],
      "text/plain": [
       "[1] 0.06128251"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(3, 1000, 0.001)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70cbda75-0104-4962-9f4a-c210f28b4259",
   "metadata": {},
   "source": [
    "## Ejercicio 17\n",
    "\n",
    "En un concurso de pesca cada pescador paga \\\\$100 por participar. La cantidad de peces obtenida por cada pescador durante el desarrollo del concurso es una v.a. con distribución de Poisson de parámetro $\\lambda$ = 4. Hay un premio de \\\\$50 por pieza. Cada pescador tiene permitido cobrar a lo sumo 6 piezas (es decir, aunque pesque más de 6 cobrará solo por 6).\n",
    "\n",
    "$X$ = \"cantidad de peces obtenida por un pescador\"\n",
    "\n",
    "$X \\sim P(4)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89d2d9c5-5a75-47ce-9ba0-c369db7e79f1",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Calcular la función de probabilidad puntual de la ganancia neta de un pescador."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "3db43125-1fda-4cf4-beca-8957cf152bb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 7 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>x</th><th scope=col>ganancia</th><th scope=col>probaPuntual</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>-100</td><td>0.01831564</td></tr>\n",
       "\t<tr><td>1</td><td> -50</td><td>0.07326256</td></tr>\n",
       "\t<tr><td>2</td><td>   0</td><td>0.14652511</td></tr>\n",
       "\t<tr><td>3</td><td>  50</td><td>0.19536681</td></tr>\n",
       "\t<tr><td>4</td><td> 100</td><td>0.19536681</td></tr>\n",
       "\t<tr><td>5</td><td> 150</td><td>0.15629345</td></tr>\n",
       "\t<tr><td>6</td><td> 200</td><td>0.21486961</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 7 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       " x & ganancia & probaPuntual\\\\\n",
       "\\hline\n",
       "\t 0 & -100 & 0.01831564\\\\\n",
       "\t 1 &  -50 & 0.07326256\\\\\n",
       "\t 2 &    0 & 0.14652511\\\\\n",
       "\t 3 &   50 & 0.19536681\\\\\n",
       "\t 4 &  100 & 0.19536681\\\\\n",
       "\t 5 &  150 & 0.15629345\\\\\n",
       "\t 6 &  200 & 0.21486961\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 7 × 3 of type dbl\n",
       "\n",
       "| x | ganancia | probaPuntual |\n",
       "|---|---|---|\n",
       "| 0 | -100 | 0.01831564 |\n",
       "| 1 |  -50 | 0.07326256 |\n",
       "| 2 |    0 | 0.14652511 |\n",
       "| 3 |   50 | 0.19536681 |\n",
       "| 4 |  100 | 0.19536681 |\n",
       "| 5 |  150 | 0.15629345 |\n",
       "| 6 |  200 | 0.21486961 |\n",
       "\n"
      ],
      "text/plain": [
       "     x ganancia probaPuntual\n",
       "[1,] 0 -100     0.01831564  \n",
       "[2,] 1  -50     0.07326256  \n",
       "[3,] 2    0     0.14652511  \n",
       "[4,] 3   50     0.19536681  \n",
       "[5,] 4  100     0.19536681  \n",
       "[6,] 5  150     0.15629345  \n",
       "[7,] 6  200     0.21486961  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 0:6\n",
    "ganancia = sapply(x, function(x) x * 50 - 100)\n",
    "probaPuntual = dpois(x, 4)\n",
    "\n",
    "# Corregimos la proba puntual para x=6 ya que debería ser P(X >= 6) = 1 - P(X <= 5)\n",
    "probaPuntual[7] = 1 - ppois(5, 4)\n",
    "\n",
    "cbind(x, ganancia, probaPuntual)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64a436fb-af57-4b8d-920e-36009dd9c59a",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "¿Cuánto dinero espera ganar cada participante?\n",
    "\n",
    "Calculemos la esperanza de la v.a. definida en la pregunta anterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "81f29d6b-1ad3-4a86-b513-ab9b0c96cb29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "90.2282709268532"
      ],
      "text/latex": [
       "90.2282709268532"
      ],
      "text/markdown": [
       "90.2282709268532"
      ],
      "text/plain": [
       "[1] 90.22827"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(ganancia * probaPuntual)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c84000af-0b1c-45f9-8c33-cb5e0f45927a",
   "metadata": {},
   "source": [
    "## Pregunta 18\n",
    "\n",
    "Sea $X$ una variable aleatoria binomial con $n = 5$ y $p = 1/3$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a985e777-da23-47c1-89f1-ba456d29a550",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Graficar la función de probabilidad puntual $p_X$ y la función de distribución acumulada $F_X$, basándose en los comandos `dbinom` y `pbinom` respectivamente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "5e01715d-0c91-4423-a9cb-9b91f8648570",
   "metadata": {},
   "outputs": [
    {
     "data": {
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ECAAAECBPoIKJD6KOlDgAABAgQIECBA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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 0:10\n",
    "n = 5\n",
    "p = 1/3\n",
    "plot(x, dbinom(x, n, p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a79bd0c7-3a4b-413d-94e0-08150b638fb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eLPzQ/Pntyps0b1/Ud7J/XFsVclBgECBAgQIECAAAECBHbppUFaPNX11rqKQYAA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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 0:10\n",
    "n = 5\n",
    "p = 1/3\n",
    "plot(x, pbinom(x, n, p), type='s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ea3f6a0-a911-49bf-b651-c24e22e8b55a",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Graficar la función de distribución acumulada de $X$ utilizando la función implementada en el ejercicio 3. Comparar con el gráfico obtenido en (a)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e37462ea-990e-4c90-bab6-9b4b9d9f468d",
   "metadata": {},
   "source": [
    "### Pregunt C\n",
    "\n",
    "Utilizando el comando `rbinom` generar 1000 realizaciones de la variable aleatoria $X$ y calcular la proporción de veces que $X$ toma los valores $0, 1, 2, 3, 4,5$. Comparar con los valores que toma la fpp."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "f3bcf86b-6400-4c7c-bcba-6ef8caf309ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 6 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>probaEstimada</th><th scope=col>probaPuntual</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>0</th><td>0.137</td><td>0.131687243</td></tr>\n",
       "\t<tr><th scope=row>1</th><td>0.329</td><td>0.329218107</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>0.321</td><td>0.329218107</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>0.166</td><td>0.164609053</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>0.043</td><td>0.041152263</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>0.004</td><td>0.004115226</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & probaEstimada & probaPuntual\\\\\n",
       "\\hline\n",
       "\t0 & 0.137 & 0.131687243\\\\\n",
       "\t1 & 0.329 & 0.329218107\\\\\n",
       "\t2 & 0.321 & 0.329218107\\\\\n",
       "\t3 & 0.166 & 0.164609053\\\\\n",
       "\t4 & 0.043 & 0.041152263\\\\\n",
       "\t5 & 0.004 & 0.004115226\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | probaEstimada | probaPuntual |\n",
       "|---|---|---|\n",
       "| 0 | 0.137 | 0.131687243 |\n",
       "| 1 | 0.329 | 0.329218107 |\n",
       "| 2 | 0.321 | 0.329218107 |\n",
       "| 3 | 0.166 | 0.164609053 |\n",
       "| 4 | 0.043 | 0.041152263 |\n",
       "| 5 | 0.004 | 0.004115226 |\n",
       "\n"
      ],
      "text/plain": [
       "  probaEstimada probaPuntual\n",
       "0 0.137         0.131687243 \n",
       "1 0.329         0.329218107 \n",
       "2 0.321         0.329218107 \n",
       "3 0.166         0.164609053 \n",
       "4 0.043         0.041152263 \n",
       "5 0.004         0.004115226 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 1000 # realizaciones\n",
    "n = 5\n",
    "p = 1/3\n",
    "probaEstimada = table(rbinom(r, n, p)) / r\n",
    "probaPuntual = dbinom(0:n, n, p)\n",
    "cbind(probaEstimada, probaPuntual)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "887277d3-8ef8-4858-9c3e-8ca97a7f5df5",
   "metadata": {},
   "source": [
    "## Ejercicio 19\n",
    "\n",
    "Las tareas llegan a una cola de un sistema de computación con un solo servidor de acuerdo con un proceso de Poisson de parámetro $\\lambda = 5$ tareas por minuto. Llamemos a dicho proceso $X_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f5ea8a9-3c9f-4090-9195-f7982bd0e676",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "¿Cuál es la probabilidad de que en 30 segundos lleguen menos de 5 tareas?\n",
    "\n",
    "$X_{0.5}$ = \"número de tareas que llegan en 30 segundos (0.5 minutos)\"\n",
    "\n",
    "$X_{0.5} \\sim P(5 * 0.5) = P(2.5)$\n",
    "\n",
    "$P(X < 5) = F_X(4) \\approx 0.891178$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "837e74de-671d-47a7-9dfb-ab81e5a13858",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.891178018914151"
      ],
      "text/latex": [
       "0.891178018914151"
      ],
      "text/markdown": [
       "0.891178018914151"
      ],
      "text/plain": [
       "[1] 0.891178"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ppois(4, 2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "895d54ba-10af-4628-9f13-85a6b071fba3",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Sea $X_1$ la cantidad de tareas recibidas en un minuto.\n",
    "\n",
    "$X_1 \\sim P(5 * 1) = P(5)$\n",
    "\n",
    "$P(X_1 \\leq 6) = F_X(6) \\approx 0.762183$\n",
    "\n",
    "$P(X_1 = 6) \\approx 0.146222$\n",
    "\n",
    "$P(X_1 \\geq 5) = 1 - P(X \\leq 4) = 1 - F_X(4) \\approx 0.559506$\n",
    "\n",
    "$P(3 \\leq X_1 \\leq 6) = F_X(6) - F_X(2) \\approx 0.637531$\n",
    "\n",
    "$P(3 < X_1 < 6) = F_X(5) - F_X(3) \\approx 0.350934$\n",
    "\n",
    "$P(3 \\leq X_1 \\leq 6 | X_1 \\geq 4) = \\frac{P((3 \\leq X_1 \\leq 6) \\cap (X_1 \\geq 4))}{P(X_1 \\geq 4)} = \\frac{P(4 \\leq X_1 \\leq 6)}{1 - P(X_1 \\leq 3)} = \\frac{F_X(6) - F_X(3)}{1 - F_X(3)} \\approx 0.676428$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "6095729c-8cfc-4103-bc8c-026aeb9866f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.762183462972939"
      ],
      "text/latex": [
       "0.762183462972939"
      ],
      "text/markdown": [
       "0.762183462972939"
      ],
      "text/plain": [
       "[1] 0.7621835"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.146222808139876"
      ],
      "text/latex": [
       "0.146222808139876"
      ],
      "text/markdown": [
       "0.146222808139876"
      ],
      "text/plain": [
       "[1] 0.1462228"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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    "ppois(6, 5)\n",
    "dpois(6, 5)\n",
    "1 - ppois(4, 5)\n",
    "ppois(6, 5) - ppois(2, 5)\n",
    "ppois(5, 5) - ppois(3, 5)\n",
    "(ppois(6, 5) - ppois(3, 5)) / (1 - ppois(3, 5))"
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    "### Pregunta C\n",
    "\n",
    "¿Cuál es el número esperado de tareas que se reciben en media hora?\n",
    "\n",
    "$X_{30}$ = \"número de tareas que llegan en 30 minutos\"\n",
    "\n",
    "$X_{30} \\sim P(5 * 30) = P(150)$\n",
    "\n",
    "$E(X) = \\lambda = 150$"
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   "source": [
    "### Pregunta D\n",
    "\n",
    "Estimar la esperanza calculada en el item anterior usando R.\n",
    "\n",
    "_Ejercicio para el lector._"
   ]
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    "## Ejercicio 20\n",
    "\n",
    "El número de veces que una red de computadoras se bloquea sigue un proceso de Poisson de parámetro igual a 2 bloqueos por semana. Hallar la probabilidad de que:"
   ]
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    "### Pregunta A\n",
    "\n",
    "En 2 semanas no se bloquee.\n",
    "\n",
    "$X_{2}$ = \"número de bloqueos en 2 semanas\"\n",
    "\n",
    "$X_{2} \\sim P(2 * 2) = P(4)$ (Nota: son 2 bloques por semana * 2 semanas)\n",
    "\n",
    "$P(X = 0) \\approx 0.018315$"
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   "source": [
    "dpois(0, 4)"
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   "source": [
    "### Pregunta B\n",
    "\n",
    "En un periodo de 4 semanas, haya exactamente 1 semana en la que no se bloquea. Sugerencia: Notar que se está preguntando por cantidad de semanas, no de bloqueos.\n",
    "\n",
    "$X_{1}$ = \"número de bloqueos en 1 semana\"\n",
    "\n",
    "$X_{1} \\sim P(2 * 1) = P(2)$\n",
    "\n",
    "$P(X=0) \\approx 0.135335$ Probabilidad de que no se bloquee en 1 semana\n",
    "\n",
    "Ahora definimos otra v.a. $Y$ = \"número de semanas donde no se bloquea el sistema\"\n",
    "\n",
    "$Y \\sim Bi(4, P(X=0)) \\approx Bi(4, 0.135335)$\n",
    "\n",
    "Con esta v.a. podemos calcular la probabilidad de que en 4 semanas, haya exactamente 1 semana en la que no se bloquea.\n",
    "\n",
    "$P(Y=1) \\approx 0.349956$"
   ]
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   "source": [
    "dbinom(1, 4, dpois(0, 2))"
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