diff --git a/Practica1_Probabilidad.ipynb b/Practica1_Probabilidad.ipynb
index 46aa9302634b5d80891801bd8b9f93bdd1a81f24..5b725b93b84401e4a4145fef8064eebecd7b2641 100644
--- a/Practica1_Probabilidad.ipynb
+++ b/Practica1_Probabilidad.ipynb
@@ -2,7 +2,6 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "preliminary-split",
    "metadata": {},
    "source": [
     "# Introducción a la probabilidad\n",
@@ -14,7 +13,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "hindu-introduction",
    "metadata": {},
    "source": [
     "## Probabilidad usando monedas\n",
@@ -25,7 +23,7 @@
     "- Lanzar una cruz\n",
     "\n",
     "Estos dos sucesos forman el espacio muestral, el conjunto de todos los sucesos posibles que pueden ocurrir. \n",
-    "Para calcular la probabilidad de que ocurra un suceso, contamos cuántas veces puede ocurrir el suceso que nos interesa (por ejemplo, que salga cara) y lo dividimos entre el espacio muestral. \n",
+    "Para calcular la probabilidad de que ocurra un suceso, contamos cuántas veces puede ocurrir el suceso que nos interesa (por ejemplo, que salga cara) y lo dividimos entre el **espacio muestral**. \n",
     "Así, la probabilidad nos dirá que una moneda ideal tendrá una probabilidad de 1 entre 2 de salir cara o cruz. \n",
     "Al observar los sucesos que pueden ocurrir, la probabilidad nos da un marco para hacer predicciones sobre la frecuencia con la que ocurrirán los sucesos. \n",
     "Sin embargo, aunque parezca obvio, si realmente intentamos lanzar algunas monedas, es probable que de vez en cuando obtengamos un número anormalmente alto o bajo de caras. \n",
@@ -34,13 +32,12 @@
     "\n",
     "## De la estadística a la probabilidad\n",
     "\n",
-    "Generaremos datos lanzando una moneda 10 veces y contando cuántas veces sale cara. Llamaremos ensayo a un conjunto de n lanzamientos de moneda (donde n es una variable que daremos). Nuestro dato será el número de caras que observemos. Puede que no obtengamos las 5 caras \"ideales\", pero no nos preocuparemos demasiado, ya que un ensayo es sólo un punto de datos. Si realizamos muchos, muchos ensayos, esperamos que el número medio de cabezas en todos nuestros ensayos se acerque al 50%. El código siguiente simula 10, 100, 1000 y 1000000 ensayos, y luego calcula la proporción media de cabezas observada. Nuestro proceso se resume también en la imagen de abajo.\n"
+    "Generaremos datos lanzando una moneda 10 veces y contando cuántas veces sale cara. Llamaremos **ensayo** a un conjunto de n lanzamientos de moneda (donde n es una variable que daremos). Nuestro dato será el número de caras que observemos. Puede que no obtengamos las 5 caras \"ideales\", pero no nos preocuparemos demasiado, ya que un ensayo es sólo un punto de datos. Si realizamos muchos, muchos ensayos, esperamos que el número medio de cabezas en todos nuestros ensayos se acerque al 50%. El código siguiente simula 10, 100, 1000 y 1000000 ensayos, y luego calcula la proporción media de cabezas observada. Nuestro proceso se resume también en la imagen de abajo.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "administrative-black",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -56,7 +53,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "acknowledged-toddler",
    "metadata": {},
    "source": [
     "La función `lanzar_moneda` es la que representa una simulación de 'n' lanzamientos de moneda.\n",
@@ -66,21 +62,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "id": "inappropriate-cleanup",
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Al lanzar la moneda 10 veces, la proporcion de vece que obtuvimos cara:  0.5\n",
+      "Al lanzar la moneda 10 veces, la proporcion de vece que obtuvimos cara:  0.3\n",
       "\n",
-      "Al lanzar la moneda 100 veces, la proporcion de vece que obtuvimos cara:  0.5\n",
+      "Al lanzar la moneda 100 veces, la proporcion de vece que obtuvimos cara:  0.55\n",
       "\n",
-      "Al lanzar la moneda 1000 veces, la proporcion de vece que obtuvimos cara:  0.517\n",
+      "Al lanzar la moneda 1000 veces, la proporcion de vece que obtuvimos cara:  0.509\n",
       "\n",
-      "Al lanzar la moneda 1000000 veces, la proporcion de vece que obtuvimos cara:  0.499648\n"
+      "Al lanzar la moneda 1000000 veces, la proporcion de vece que obtuvimos cara:  0.499319\n"
      ]
     }
    ],
@@ -96,7 +91,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "directed-longitude",
    "metadata": {},
    "source": [
     "A continuación, la funcion `experimentos` repite estos ensayos de lanzar la moneda unas 100 veces el número de veces que queramos, devolviendo el número medio de cabezas en cada ensayo. "
@@ -105,7 +99,6 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "metric-lemon",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -118,7 +111,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "motivated-insight",
    "metadata": {},
    "source": [
     "Las simulaciones de lanzamiento de monedas nos dan algunos resultados interesantes.\n",
@@ -128,26 +120,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
-   "id": "resident-small",
+   "execution_count": 95,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Con 10 experimentos, valor medio: 0.5 desviación estandar: 0.1247219128924647\n",
+      "Con 10 experimentos, valor medio: 0.57 desviación estandar: 0.170293863659264\n",
       "\n",
-      "Con 100 experimentos, valor medio: 0.506 desviación estandar: 0.14129273287623947\n",
+      "Con 100 experimentos, valor medio: 0.537 desviación estandar: 0.15219272736443834\n",
       "\n",
-      "Con 1000 experimentos, valor medio: 0.5046 desviación estandar: 0.16007643319509735\n",
+      "Con 1000 experimentos, valor medio: 0.4974 desviación estandar: 0.15419797993818535\n",
       "\n",
-      "Con 100000 experimentos, valor medio: 0.500633 desviación estandar: 0.15795932648149721\n"
+      "Con 100000 experimentos, valor medio: 0.499653 desviación estandar: 0.15837686202000667\n"
      ]
     },
     {
      "data": {
-      "image/png": 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rW+guoC+RZGeS2SSzR48eXUEZkqRptNyA+izwy8BZwNPAJ5f6Bt7tU5L0cpYVUFX1bFX9pKp+CnyOn03jLXQXUEmSlmRZAXXs1tWd3wKOneG3F7g8yb9JcgawBfjaykqUJK1Hi96wMMkXgXOBDUkOA9cC5yY5CyjgCeA/AVTVg0luBh4CXgCurqqf9FK5JGmqLRpQVXXFPM2ff5n+fwz88UqKkiTJK0lIkppkQEmSmmRASZKaZEBJkppkQEmSmmRASZKaZEBJkppkQC3DzK59zOzaN+kyJGmqGVCSpCYZUBob9zwlLYUBJUlqkgElSWqSASWpOU4HL8+0fW4GlCSpSYsGVJIbkhxJ8q2htpOT7E9yqPt5UteeJJ9O8miS+5O8pc/iJUnTa5Q9qBuB7XPadgEHqmoLcKBbB3gXg7vobgF2Ap9dnTIlSevNogFVVXcBz81pvgTY0y3vAS4dav9CDRwEXjvn9vDS1FutWYckO7r+h5LsGGr/9SQPdK/5dJKM918ojcdyj0Ftqqqnu+VngE3d8qnAd4b6He7aXiLJziSzSWaPHj26zDKkJt3ICmcdkpwMXAu8FTgbuPZYqHV9PjD0urnbkqbCik+SqKoCahmv211V26pq28aNG1dahtSMVZp1eCewv6qeq6rngf3A9u6511TVwW7sfWHovaSpstyAevbY1F3380jX/hRw2lC/zV2btN4tddbh5doPz9P+Es5SaK1bbkDtBY7Nie8Abhlqf183r34O8P2hQSmJ5c86LGM7zlJoTRvlNPMvAl8F3pjkcJKrgOuBC5McAi7o1gFuBR4HHgU+B3yol6qltWepsw4v1755nnZp6hy/WIequmKBp86fp28BV6+0KGkKHZt1uJ6Xzjpck+QmBidEfL+qnk5yO/Dfhk6MuAj4SFU9l+QH3QzF3cD7gP8xzn+INC6LBpSkpelmHc4FNiQ5zOBsvOuBm7sZiCeBy7rutwIXM5h1+BHwOwBdEH0c+HrX72NVdezEiw8xOFPw1cBt3UOaOgaUtMpWa9ahqm4AbpinfRY4cyU1SmuB1+KTJDXJgJIkNcmAkiQ1yYCSJDXJgJIkNcmAkiQ1yYCSJDXJgJIkNcmAkiQ1yYCSJDXJgJIkNWlF1+JL8gTwQ+AnwAtVta27VfWXgBngCeCy7o6gkiSNbDX2oN5RVWdV1bZufRdwoKq2AAe6dUmSlqSPKb5LgD3d8h7g0h62IUmacisNqAL+T5J7kuzs2jYN3eb9GWDTfC9MsjPJbJLZo0ePrrAMrSczu/Yxs2vfpMuQ1LOV3g/qP1TVU0leB+xP8vfDT1ZVJan5XlhVu4HdANu2bZu3jyRp/VrRHlRVPdX9PAL8NXA28GySUwC6n0dWWqQkaf1ZdkAl+bdJTjy2DFwEfAvYC+zouu0AbllpkavFqSFJWjtWsge1Cfhykm8CXwP2VdXfAtcDFyY5BFzQrUtaB/wCOB1a+TK/7GNQVfU48GvztP8/4PyVFCVJkleSkCQ1yYCSJDXJgJIkNcmAkiQ1yYCSJDXJgJIkNcmAkiQ1yYCSJDXJgJIkNcmAkiQ1yYCSJDXJgJIkNcmA0rrWwhWbJc3PgJJkUKs3K/nd6i2gkmxP8kiSR5PsWsl7OXikF1vN8SW1qpeASnIc8BngXcBW4IokW/vYlrTeOL60XvS1B3U28GhVPV5V/wLcBFzS07ak9cbxpXUhVbX6b5q8B9heVb/brb8XeGtVXTPUZyews1t9I/DIqhcyvw3Ad8e0raWwrqUZZ12vr6qNY9rWokYZX127Y+zFrGtpJj7Gln3L95Wqqt3A7nFvN8lsVW0b93YXY11L02pdLXGMvZh1LU0LdfU1xfcUcNrQ+uauTdLKOb60LvQVUF8HtiQ5I8kJwOXA3p62Ja03ji+tC71M8VXVC0muAW4HjgNuqKoH+9jWMox9ymNE1rU0rdbVu8bHF7T7f2NdSzPxuno5SUKSpJXyShKSpCYZUJKkJk1tQC12KZgkf5DkoST3JzmQ5PUt1DXU77eTVJKxnOY5Sl1JLus+sweT/HkLdSU5PckdSe7t/i8vHkdd612r42uU2ob6OcZGqGuiY6yqpu7B4MDxY8AvAScA3wS2zunzDuDnuuUPAl9qoa6u34nAXcBBYFsLdQFbgHuBk7r11zVS127gg93yVuCJSf/+Tfuj1fE1am1dP8fY6HVNbIxN6x7UopeCqao7qupH3epBBn9LMvG6Oh8HPgH88xhqGrWuDwCfqarnAarqSCN1FfCabvkXgH8cQ13rXavja6TaOo6x0eua2Bib1oA6FfjO0Prhrm0hVwG39VrRwKJ1JXkLcFpVjfMS7qN8Xm8A3pDkK0kOJtneSF3XAVcmOQzcCvzeGOpa71odX+AY66Ou65jQGJvYpY5akeRKYBvwGw3U8grgU8D7J1zKfI5nMAVxLoNvw3cl+dWq+t4kiwKuAG6sqk8meRvwp0nOrKqfTrgu0db4AsfYMk1sjE3rHtRIl4JJcgHwUeDdVfXjBuo6ETgTuDPJE8A5wN4xHMQd5fM6DOytqn+tqm8D/8BgME26rquAmwGq6qvAqxhc5FL9aXV8jVKbY2zpdU1ujI3rYNc4Hwy+iTwOnMHPDvy9aU6fNzM4OLilpbrm9L+T8RzAHeXz2g7s6ZY3MJgW+MUG6roNeH+3/CsM5scz6d/BaX60Or5GrW1Of8dYw2NsbL84434AFzP4BvIY8NGu7WMMvs0B/B3wLHBf99jbQl1z+o5l8Iz4eYXB1MhDwAPA5Y3UtRX4Sjew7gMumvTv3np4tDq+RqltTl/HWMNjzEsdSZKaNK3HoCRJa5wBJUlqkgElSWqSASVJapIBJUlqkgElSWqSASVJatL/BzdXSMgge6kBAAAAAElFTkSuQmCC\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 4 Axes>"
       ]
@@ -188,7 +179,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "organic-aside",
    "metadata": {},
    "source": [
     "En 10 ensayos, hay un ligero error, pero este error desaparece casi por completo con 1.000.000 experimentos. \n",
@@ -198,7 +188,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bound-citizenship",
    "metadata": {},
    "source": [
     "## Preguntas\n",
@@ -212,7 +201,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "norwegian-channels",
    "metadata": {},
    "source": [
     "## Ensayos de Bernulli\n",
@@ -226,29 +214,47 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "id": "interior-alarm",
+   "execution_count": 73,
    "metadata": {},
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "array([1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0])"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "With bernoulli library:\n",
+      "[0 1 0 1 1 0 0 1 0 1 1 1 0 0 0]\n",
+      "With my functions:\n",
+      "[0 0 1 1 0 1 0 0 1 0 1 0 1 1 0]\n"
+     ]
     }
    ],
    "source": [
     "from scipy.stats import bernoulli\n",
-    "bernoulli.rvs(size=15,p=0.5)"
+    "import numpy as np\n",
+    "\n",
+    "print(\"With bernoulli library:\")\n",
+    "print(bernoulli.rvs(size=15,p=0.5))\n",
+    "\n",
+    "def bern(p,x):\n",
+    "    be = p**x*(1-p)**(1-x)\n",
+    "    return be\n",
+    "\n",
+    "def bern_exp(p,n):\n",
+    "    exp = []\n",
+    "    for i in range(n):\n",
+    "        if random.random() < bern(p,1):\n",
+    "             x = 1 # Éxito: cara\n",
+    "        else:\n",
+    "            x = 0 # Fracaso: sello\n",
+    "        exp.append(x)\n",
+    "    return np.array(exp)\n",
+    "    \n",
+    "print(\"With my functions:\")    \n",
+    "print(bern_exp(p=0.5,n=15))"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "square-entry",
    "metadata": {},
    "source": [
     "## Ejercicios"
@@ -256,10 +262,9 @@
   },
   {
    "cell_type": "markdown",
-   "id": "addressed-compiler",
    "metadata": {},
    "source": [
-    "Los siguientes ejercicios deben ser realizados durante la sesión practica. Lo ideal seria hacer el calculo de la probabilidad, simular los experimentos y comparar los resultados. Para las simulaciones podemos usar las funciones definidas antes e implementar algunas modificaciones.\n",
+    "Los siguientes ejercicios deben ser realizados durante la sesión practica. Lo ideal seria hacer el cálculo de la probabilidad, simular los experimentos y comparar los resultados. Para las simulaciones podemos usar las funciones definidas antes e implementar algunas modificaciones.\n",
     "\n",
     "Los ejercicios están basados en el siguiente escenario:\n",
     "\n",
@@ -268,7 +273,6 @@
   },
   {
    "cell_type": "markdown",
-   "id": "familiar-ancient",
    "metadata": {},
    "source": [
     "1. El experimento consiste en  alatoreamente sacar una moneda de la bolsa, lanzarla, anotar el resultado y volver a introducir la moneda en la bolsa. Repites esta acción hasta haber lanzado monedas unas 21 veces. Preguntas:\n",
@@ -278,22 +282,236 @@
     "    - Estimar qué desviación esperas entre experimento y experimento. "
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 149,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Calculo analítico:\n",
+      "- El número de caras más probable es  7 caras, con una probabilidad de 0.18203351708086507 \n",
+      "\n",
+      "Simulación:\n",
+      "- Con 100 experimentos, valor medio: 0.349 desviación estandar: 0.04695796529930258\n",
+      "- Entonces en promedio salieron 7.329 caras\n",
+      "\n",
+      "Se espera tener una desviación de  2.1655869104394463\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def factorial(x):\n",
+    "    if x==0:\n",
+    "        return 1\n",
+    "    return x*factorial(x-1)\n",
+    "\n",
+    "def combinatorial(n,x):\n",
+    "    comb = factorial(n)/(factorial(x)*factorial(n-x))\n",
+    "    return comb\n",
+    "\n",
+    "def binomial(p,n,x):\n",
+    "    bi = combinatorial(n,x)*p**x*(1-p)**(n-x)\n",
+    "    return bi\n",
+    "\n",
+    "def bin_exp(p,n):\n",
+    "    x_val = []\n",
+    "    exp = []\n",
+    "    suma = 0\n",
+    "    for i in range(n+1):\n",
+    "        aux = binomial(p,n,i)\n",
+    "        x_val.append(i)\n",
+    "        exp.append(aux)\n",
+    "    return np.array(exp), x_val\n",
+    "\n",
+    "def experimentos_bin(n,n_lanzamientos):\n",
+    "    experimento = []\n",
+    "    for i in range(n):\n",
+    "        experimento.append(lanzar_moneda_bin(n_lanzamientos))\n",
+    "    return (experimento)\n",
+    "\n",
+    "def lanzar_moneda_bin(n):\n",
+    "    cara = 0\n",
+    "    p = 2/3*0.5 + 1/3*0.01\n",
+    "    for i in range(n):\n",
+    "        if random.random() <= p:\n",
+    "            cara +=1      \n",
+    "    return cara/n\n",
+    "\n",
+    "p = 2/3*0.5 + 1/3*0.01\n",
+    "\n",
+    "# ITEM A: cálculo analítico\n",
+    "exp,x = bin_exp(p=p,n=21)\n",
+    "aux = np.where(exp == np.max(exp))\n",
+    "aux = aux[0][0]\n",
+    "print(\"Calculo analítico:\")\n",
+    "print(\"- El número de caras más probable es \",x[aux],\"caras, con una probabilidad de\",np.max(exp),'\\n')\n",
+    "\n",
+    "# ITEM B: Simulación\n",
+    "n_lanzamientos = 100\n",
+    "ex_100 = experimentos_bin(n=100, n_lanzamientos=n_lanzamientos)\n",
+    "n_bins = 100\n",
+    "print('Simulación:')\n",
+    "print ('- Con 100 experimentos, valor medio:',mean(ex_100), 'desviación estandar:', stdev(ex_100))\n",
+    "print('- Entonces en promedio salieron',mean(ex_100)*21,'caras\\n')\n",
+    "\n",
+    "#ITEM C: Desviación entre experimentos\n",
+    "print('Se espera tener una desviación de ',(21*p*(1-p))**0.5)\n",
+    "\n",
+    "fig, axs = plt.subplots(1, 2, tight_layout=True)\n",
+    "axs[0].set_xlabel(\"Número de caras en 21 intentos\")\n",
+    "axs[0].set_ylabel(\"Probabilidad\")\n",
+    "axs[0].plot(x,exp,\".\")\n",
+    "axs[1].set_xlabel(\"Prob. de salir cara\")\n",
+    "axs[1].set_ylabel(\"Frecuencia\")\n",
+    "axs[1].hist(ex_100, bins=n_bins, range=[0.1,0.9])\n",
+    "plt.show()"
+   ]
+  },
   {
    "cell_type": "markdown",
-   "id": "concerned-lending",
    "metadata": {},
    "source": [
     "2. El experimento consiste en alatoreamente sacar una moneda de la bolsa, lanzarla, y luego sacar las dos monedas que quedan en la bolsa, lanzarlas y anotar los resultado\n",
     " Repites esta acción hasta haber lanzado monedas unas 21 veces. Preguntas:\n",
     "\n",
-    "    - ¿En qué sentido este ejemplo es distinto a 1?\n",
+    "    - ¿En qué sentido este ejemplo es distinto a 1?\\\n",
+    "        **En este caso la probabilidad de que salga cara varía en cada extracción.**\n",
     "    - Simular 100 experimentos para estimar cuantas caras esperas obtener en un experimento.  \n",
     "    - Estimar qué desviación esperas entre experimento y experimento. "
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 164,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Calculo analítico:\n",
+      "- 1ra moneda: El número de caras más probable es  7 caras, con una probabilidad de 0.18203351708086507 \n",
+      "\n",
+      "- 2da moneda: El número de caras más probable es  5 caras, con una probabilidad de 0.19758061728439202 \n",
+      "\n",
+      "- 3ra moneda: El número de caras más probable es  5 caras, con una probabilidad de 0.19758061728439202 \n",
+      "\n"
+     ]
+    },
+    {
+     "data": {
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\n",
+      "text/plain": [
+       "<Figure size 1080x360 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#ITEM B\n",
+    "def factorial(x):\n",
+    "    if x==0:\n",
+    "        return 1\n",
+    "    return x*factorial(x-1)\n",
+    "\n",
+    "def combinatorial(n,x):\n",
+    "    comb = factorial(n)/(factorial(x)*factorial(n-x))\n",
+    "    return comb\n",
+    "\n",
+    "def binomial(p,n,x):\n",
+    "    bi = combinatorial(n,x)*p**x*(1-p)**(n-x)\n",
+    "    return bi\n",
+    "\n",
+    "def bin_exp(p,n):\n",
+    "    x_val = []\n",
+    "    exp = []\n",
+    "    suma = 0\n",
+    "    for i in range(n+1):\n",
+    "        aux = binomial(p,n,i)\n",
+    "        x_val.append(i)\n",
+    "        exp.append(aux)\n",
+    "    return np.array(exp), x_val\n",
+    "\n",
+    "def experimentos_bin(n,n_lanzamientos):\n",
+    "    experimento = []\n",
+    "    for i in range(n):\n",
+    "        experimento.append(lanzar_moneda_bin(n_lanzamientos))\n",
+    "    return (experimento)\n",
+    "\n",
+    "def lanzar_moneda_bin(n):\n",
+    "    cara = 0\n",
+    "    p = 2/3*0.5 + 1/3*0.01\n",
+    "    for i in range(n):\n",
+    "        if random.random() <= p:\n",
+    "            cara +=1      \n",
+    "    return cara/n\n",
+    "\n",
+    "p1 = 2/3*0.5 + 1/3*0.01\n",
+    "p2 = 1/2*0.5 + 1/2*0.01\n",
+    "p3 = 1/2*0.5 + 1/2*0.01\n",
+    "exp,x = bin_exp(p=p1,n=21)     # Probability distribution of the first coin, to be face\n",
+    "exp2,x2 = bin_exp(p=p2,n=21)   # Probability distribution of the second coin, to be face\n",
+    "exp3,x3 = bin_exp(p=p3,n=21)   # Probability distribution of the third coin, to be face\n",
+    "aux = np.where(exp == np.max(exp))\n",
+    "aux = aux[0][0]\n",
+    "aux2 = np.where(exp2 == np.max(exp2))\n",
+    "aux2 = aux2[0][0]\n",
+    "aux3 = np.where(exp3 == np.max(exp3))\n",
+    "aux3 = aux3[0][0]\n",
+    "print(\"Calculo analítico:\")\n",
+    "print(\"- 1ra moneda: El número de caras más probable es \",x[aux],\"caras, con una probabilidad de\",np.max(exp),'\\n')\n",
+    "print(\"- 2da moneda: El número de caras más probable es \",x[aux2],\"caras, con una probabilidad de\",np.max(exp2),'\\n')\n",
+    "print(\"- 3ra moneda: El número de caras más probable es \",x[aux3],\"caras, con una probabilidad de\",np.max(exp3),'\\n')\n",
+    "print(\"- Entonces  \",x[aux3],\"caras, con una probabilidad de\",np.max(exp3),'\\n')\n",
+    "\n",
+    "# ITEM B: Simulación\n",
+    "#n_lanzamientos = 100\n",
+    "#ex_100 = experimentos_bin(n=100, n_lanzamientos=n_lanzamientos)\n",
+    "#n_bins = 100\n",
+    "#print('Simulación:')\n",
+    "#print ('- Con 100 experimentos, valor medio:',mean(ex_100), 'desviación estandar:', stdev(ex_100))\n",
+    "#print('- Entonces en promedio salieron',mean(ex_100)*21,'caras\\n')\n",
+    "\n",
+    "#ITEM C: Desviación entre experimentos\n",
+    "#print('Se espera tener una desviación de ',(21*p*(1-p))**0.5)\n",
+    "\n",
+    "fig, axs = plt.subplots(1, 3, constrained_layout=True,figsize=(15,5))\n",
+    "axs[0].set_title('1ra moneda')\n",
+    "axs[0].set_xlabel(\"Número de caras en 21 intentos\")\n",
+    "axs[0].set_ylabel(\"Probabilidad\")\n",
+    "axs[0].plot(x,exp,\".\")\n",
+    "axs[1].set_title('2da moneda')\n",
+    "axs[1].set_xlabel(\"Número de caras en 21 intentos\")\n",
+    "axs[1].set_ylabel(\"Probabilidad\")\n",
+    "axs[1].plot(x,exp,\".\")\n",
+    "axs[2].set_title('3ra moneda')\n",
+    "axs[2].set_xlabel(\"Número de caras en 21 intentos\")\n",
+    "axs[2].set_ylabel(\"Probabilidad\")\n",
+    "axs[2].plot(x,exp,\".\")\n",
+    "plt.show()"
+   ]
+  },
   {
    "cell_type": "markdown",
-   "id": "acoustic-society",
    "metadata": {},
    "source": [
     "3. Sacamos la primera moneda. \n",