exercicio_1-3_lista.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e3077c46",
   "metadata": {},
   "source": [
    "## Exercise 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "40af35cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import interpolation \n",
    "import numpy as np\n",
    "import scipy as sc\n",
    "import scipy.stats\n",
    "from scipy.special import erf\n",
    "import random as rd\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "def third_function_pdf(x,x0, sigma):\n",
    "    numerator = np.exp(-np.power(x - x0, 2.) / (2 * sigma**2)) * (1/ (sigma*np.sqrt(2 * np.pi))) - np.exp(-np.power(x + x0, 2.)/ (2 * sigma**2)) * (1/ (sigma * np.sqrt(2 * np.pi)))\n",
    "    return erf(x0/math.sqrt(2*sigma)) * numerator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45beb329",
   "metadata": {},
   "source": [
    "Interpolating the functions\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e84ba3ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf_object = interpolation.PDF()\n",
    "x_gauss = np.linspace(-5, 5, 500)\n",
    "y_gauss = [pdf_object.gaussian_oned_pdf(a,0,1) for a in x_gauss]\n",
    "gauss_generator = interpolation.LinearInterp(x_gauss, y_gauss, [-3,3])\n",
    "\n",
    "x_third = np.linspace(0, 10, 500)\n",
    "y_third = [third_function_pdf(a, 4, 1) for a in x_third]\n",
    "third_generator = interpolation.LinearInterp(x_third, y_third,[0,10])\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8512c072",
   "metadata": {},
   "source": [
    "We do the same procedure for all the possible $N$. First, generate $N$ points using our interpolation. Then, binning the lists of points for each distribution. Next, we compute the relative error for the expected number of points in each bin and make plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "45e1528b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wM0ucg8DMLHEOAjOzxDkIzMwS5yAwM0ucg8DMLHG5BoGkxZJekLRN0jUV2nxQ0vOSNkv6Wp71mJnZwca8VeWhklQP3Ar8FtAFrJO0Orsr2VCbBcAngV+LiB5JJ+RVj5mZjSzPEcHZwLaI6IiIPuAe4MJhba4Abo2IHoCI2JVjPWZmNoI8g2A20Fm23pVtK7cQWCjpe5LWSlo80oEkLZfULqm9u7s7p3LNzNJU9GRxA7AAWAQsBW6XdNzwRhGxIiLaIqKtubm5thWamU1zeQbBTqClbH1Otq1cF7A6IvZHxI+ArZSCwczMaiTPIFgHLJB0oqRG4GJg9bA236Q0GkBSE6VLRR051mRmZsPkFgQR0Q9cCTwMbAHujYjNkm6UtCRr9jCwW9LzwKPAJyJid141mZnZwRQRRdcwLm1tbdHe3l50GWZmU4qk9RHRNtK+oieLzcysYA4CM7PEOQjMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBLnIDAzS1yuQSBpsaQXJG2TdM0o7T4gKSSNeNMEMzPLT25BIKkeuBU4HzgJWCrppBHaHQP8T+DJvGoxM7PK8hwRnA1si4iOiOgD7gEuHKHdTcBngddzrMXMzCrIMwhmA51l613Ztl+QdAbQEhEPjnYgScsltUtq7+7unvhKzcwSVthksaQ64Bbg6rHaRsSKiGiLiLbm5ub8izMzS0ieQbATaClbn5NtG3IMcArwmKTtwLnAak8Ym5nVVp5BsA5YIOlESY3AxcDqoZ0R0RsRTRHRGhGtwFpgSUS051iTmZkNk1sQREQ/cCXwMLAFuDciNku6UdKSvJ7XzMzGpyHPg0fEGmDNsG3XV2i7KM9azMxsZH5nsZlZ4hwEZmaJcxCYmSXOQWBmljgHgZlZ4hwEZmaJcxCYmSXOQWBmljgHgZlZ4hwEZmaJcxCYmSXOQWBmljgHgZlZ4hwEZmaJcxCYmSUu1yCQtFjSC5K2SbpmhP1XSXpe0rOSHpE0L896zMzsYLkFgaR64FbgfOAkYKmkk4Y12wC0RcQ7gPuAz+VVj5mZjSzPEcHZwLaI6IiIPuAe4MLyBhHxaETszVbXUrrBvZmZ1VCeQTAb6Cxb78q2VXIZ8FCO9ZiZ2QhyvWdxtSRdArQB76mwfzmwHGDu3Lk1rMzMbPrLc0SwE2gpW5+TbTuApPOAa4ElEbFvpANFxIqIaIuItubm5lyKNTNLVZ5BsA5YIOlESY3AxcDq8gaSTge+RCkEduVYi5mZVZBbEEREP3Al8DCwBbg3IjZLulHSkqzZzcDRwDckbZS0usLhzMwsJ7nOEUTEGmDNsG3Xly2fl+fzm5nZ2PzOYjOzxDkIzMwS5yAwM0ucg8DMLHEOAjOzxCUTBOt39HDro9tYv6On6FIO1PkUPPE3pX8nmY27NrJy00o27tpYdCkH2LthA69+aQV7N2woupQDvNzRy/pvb+fljt6iSznAS1u38OT/vZeXtm4puhQ7DL29T7N9+xfp7X16wo89KT5iIm/rd/TwoZVr6esfpLGhjq9efi5nzptVdFmlX/53LoGBPqhvhGWroeXsoqsCSiFwxXeuoG+gj8b6Rm7/7dt55wnvLLos9m7YwIsf+UOirw81NjL3y3dw1OmnF10WL3f08q2/3cBA/yD1DXVc+PHT+aX5M4sui5e2buEbN13LQH8/9Q0N/P6nPsNbF7696LJsnHp7n+bpDR9mcLCPurpGzjj9LmbOPGPCjp/EiGBtx276+gcZDNjfP8jajt1Fl1Sy/YlSCMRA6d/tTxRd0S+0v9JO30Afgwyyf3A/7a+0F10SAHufWkf09cHgILF/P3ufWld0SQDs3NrDQP8gETAwMMjOrZNj5Nm5eRMD/f3E4CAD/f10bt5UdEl2CHp6nmRwsA8YZHBwPz09T07o8ZMIgnPnH09jQx31ghkNdZw7//iiSyppfXdpJKD60r+t7y66ol9oe3MbjfWN1KueGXUzaHtzW9ElAXDU2Wehxkaor0czZnDU2WcVXRIAsxfOor6hDtVBfX0dsxdOghEn0HLyqdQ3NKC6OuobGmg5+dSiS7JDMGvWOdTVNQL11NXNYNascyb0+IqICT1g3tra2qK9ffx/na7f0cPajt2cO//4yXFZaEjnU6WRQOu7J81loSEbd22k/ZV22t7cNikuCw3Zu2EDe59ax1FnnzUpLgsNebmjl51be5i9cNakuCw05KWtW+jcvImWk0/1ZaEprLf3aXp6nmTWrHMO6bKQpPURMeJfdMkEgZlZykYLgiQuDZmZWWUOAjOzxDkIzMwS5yAwM0ucg8DMLHEOAjOzxE25l49K6gZ2HOLDm4BXJ7Cc6cB9ciD3x8HcJweaqv0xLyKaR9ox5YLgcEhqr/Q62lS5Tw7k/jiY++RA07E/fGnIzCxxDgIzs8SlFgQrii5gEnKfHMj9cTD3yYGmXX8kNUdgZmYHS21EYGZmwzgIzMwSNy2DQNJiSS9I2ibpmhH2HyHp69n+JyW1FlBmTVXRJ1dJel7Ss5IekTSviDprZaz+KGv3AUkhaVq9XHAk1fSJpA9m3yebJX2t1jXWUhU/M3MlPSppQ/Zzc0ERdU6IiJhWX0A98O/AfKAReAY4aVibPwZuy5YvBr5edN2ToE/eCxyVLX90OvdJNf2RtTsGeBxYC7QVXXfRfQIsADYAs7L1E4quu+D+WAF8NFs+CdhedN2H+jUdRwRnA9sioiMi+oB7gAuHtbkQuDNbvg94nyTVsMZaG7NPIuLRiNibra4F5tS4xlqq5nsE4Cbgs8DrtSyuINX0yRXArRHRAxARu2pcYy1V0x8BHJstzwReqmF9E2o6BsFsoLNsvSvbNmKbiOgHeoFJciPjXFTTJ+UuAx7KtaJijdkfks4AWiLiwVoWVqBqvkcWAgslfU/SWkmLa1Zd7VXTH58GLpHUBawBPlab0iZeQ9EF2OQi6RKgDXhP0bUURVIdcAtwacGlTDYNlC4PLaI0Ynxc0qkR8R9FFlWgpcCqiPgbSb8K3CXplIgYLLqw8ZqOI4KdQEvZ+pxs24htJDVQGtbtrkl1xaimT5B0HnAtsCQi9tWotiKM1R/HAKcAj0naDpwLrJ7mE8bVfI90AasjYn9E/AjYSikYpqNq+uMy4F6AiPgBcCSlD6SbcqZjEKwDFkg6UVIjpcng1cParAaWZcsXAd+NbMZnmhqzTySdDnyJUghM52u/MEZ/RERvRDRFRGtEtFKaM1kSEe3FlFsT1fzcfJPSaABJTZQuFXXUsMZaqqY/XgTeByDp7ZSCoLumVU6QaRcE2TX/K4GHgS3AvRGxWdKNkpZkzf4BOF7SNuAqoOLLB6eDKvvkZuBo4BuSNkoa/k0/bVTZH0mpsk8eBnZLeh54FPhEREzLkXSV/XE1cIWkZ4C7gUun6h+U/ogJM7PETbsRgZmZjY+DwMwscQ4CM7PEOQjMzBLnIDAzS5yDwKwKkgayl9U+I+lpSe/Ktr9V0n1F12d2OPzyUbMqSHotIo7Oln8H+IuISPZjOGx68YjAbPyOBXoAJLVKei5bvlTSA5K+LemHkj6Xba+XtErSc5I2Sfp4gbWbHcQfOmdWnTdI2kjpYwTeAvxmhXbvBE4H9gEvSPo74ARgdkScAiDpuLyLNRsPjwjMqvPziHhnRLwNWAz8Y4V7WDySfVbR68DzwDxKn8czX9LfZR/dvKd2ZZuNzUFgNk7ZJ002Ac0j7C7/1NYBoCG7kctpwGPAHwEr867RbDx8achsnCS9jdKtDHcDR1XRvgnoi4j7Jb0AfCXnEs3GxUFgVp2hOQIAAcsiYqDKO5zOBr6c3fAG4JM51Gd2yPzyUTOzxHmOwMwscQ4CM7PEOQjMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBL3/wEZLsIxLcotqgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WESuAFSOWfXSMbU/IsxYzMxtdYYPFZmY2MTgIzMwS5yAwM0ucg8DMLHEOAjOzxDkIzMwS5yAwM0ucg8DMLHEOAjOzxDkIzMwS5yAwM0ucg8DMLHEOAjOzxDkIzMwS5yAwM0ucg8DMLHEOArMm9+CG9dz53et5cMP6okuxCSrXJ5SZWbEe3LCeb3/ywwwODFBqbeXNF32Kw+cfWXRZNsG4RWDWxHrX3cvgwAAxNMTgwAC96+4tuiSbgBwEZk2sY8HRlFpbUUsLpdZWOhYcXXRJNgG5a8isiR0+/0jefNGn6F13Lx0Ljna3kI3KQWDW5A6ff6QDwKpy15CZWeIcBGZmiXMQmJklzkFgZpY4B4GZWeIcBGZmiXMQWEPZtWYND391KbvWrCm6FLOm4esIrGHsWrOGB95+FtHfj9ramP21K5i8cGHRZZk1PLcIrGHsWnUX0d8PQ0PE7t3sWnVX0SWZNQUHgTWMyYuPRW1tUCqhSZOYvPjYoksyawruGrKGMXnhQmZ/7Qp2rbqLyYuPdbeQWZ3kGgSSTgS+AJSAZRHx6RHrLwDOBgaA7cBZEbE5z5qssU1euNABYFZnuXUNSSoBlwInAUcBp0k6asRma4CuiHgecAPw2bzqMTOz0eU5RrAY2BgRPRHRD1wHnFK5QUTcEhG7stmVwKwc6zEzs1HkGQQzgd6K+S3ZsrG8A/iv0VZIOldSt6Tu7du317FEMzObEGcNSXor0AV8brT1EbE0Iroioqu9vX18izMza3J5DhZvBToq5mdly55E0quBDwMvj4gncqzHzKxh7dhxN319dzJ9+guZNm1RXfedZxDcBcyTdATlADgVOL1yA0kLga8CJ0bEthxrMTNrWDt23M3da97G0FA/LS1tLFp4dV3DILeuoYgYAM4DbgLWA9dHxDpJF0s6Odvsc8AU4NuS1kpanlc9ZmaNqq/vToaG+oEhhoZ209d3Z133n+t1BBGxAlgxYtlHK6Zfnefnm5k1g+nTX0hLSxtDQ7tpaZnE9OkvrOv+fWWxmdkEN23aIhYtvLohxwjMzKxOpk1bVPcAGDYhTh81M7PiOAjMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBLnIDAzS5yDwMwscQ6CovWugtv/tfw6gazdtpZl9y5j7ba1RZdiZjnzE8qK1LsKrjwZBvuh1AZLlkPH4qKrYu22tZxz8zn0D/bTVmrjstdexjGHHFN0WWaWE7cIirTp9nIIxGD5ddPtRVcEQPdvu+kf7GeIIXYP7ab7t91Fl2RmOXIQFKnzpeWWgErl186XFl0RAF2HdtFWaqOkEpNaJtF1aFfRJU14D/XsYPWPNvFQz46iSzHbZ4qIomvYJ11dXdHd3UTfUHtXlVsCnS+dEN1Cw9ZuW0v3b7vpOrTL3UJ78VDPDr7/b2sYHBii1NrCKe9byLPmTiu6LLMnkbQ6Ikb9VucxgqJ1LJ5QATDsmEOOcQDUaOuGPgYHhoiAwcEhtm7ocxBYQ3HXkNnTNHP+dEqtLagFSqUWZs6fXnRJZvvELQKzp+lZc6dxyvsWsnVDHzPnT3drwBqOg8CsDp41d5oDwBqWu4bMzBLnIDAzS5yDwMwscQ4CM7PEOQjMzBLnIDAzS1zD3WJC0nZg81N8+wzg4TqWMxH5GJtDCscIaRznRDnGORHRPtqKhguCp0NS91j32mgWPsbmkMIxQhrH2QjH6K4hM7PEOQjMzBKXWhAsLbqAceBjbA4pHCOkcZwT/hiTGiMwM7M9pdYiMDOzERwEZmaJSyIIJF0haZukXxRdS14kdUi6RdJ9ktZJOr/omupN0v6SVkm6JzvGTxRdU14klSStkfSfRdeSB0mbJN0raa2kJnr27J9JOkjSDZJ+KWm9pBcVXdNYkhgjkPQyYCdwVUQ8t+h68iDpMOCwiLhb0oHAauBvIuK+gkurG0kCDoiInZImAT8Fzo+IlQWXVneSLgC6gKkR8fqi66k3SZuAroiYCBda5ULSlcDtEbFMUhswOSJ+X3BZo0qiRRARtwG/K7qOPEXEbyLi7mz6D8B6YGaxVdVXlO3MZidlP033TUbSLOCvgWVF12JPjaRpwMuAywEion+ihgAkEgSpkdQJLATuLLiUusu6TNYC24AfR0TTHSPweeCDwFDBdeQpgJslrZZ0btHF5OAIYDvwtayLb5mkA4ouaiwOgiYjaQrwHeAfI+LRouupt4gYjIhjgFnAYklN1dUn6fXAtohYXXQtOXtJRCwCTgLenXXfNpNWYBHwlYhYCDwGfKjYksbmIGgiWb/5d4BrIuLGouvJU9bMvgU4seBS6u144OSsD/064JWSvlFsSfUXEVuz123Ad4HFxVZUd1uALRUt1hsoB8OE5CBoEtlA6uXA+oi4pOh68iCpXdJB2fQzgNcAvyy0qDqLiAsjYlZEdAKnAv8TEW8tuKy6knRAdkIDWXfJa4GmOqMvIh4CeiX9ZbboVcCEPXGjtegCxoOka4ETgBmStgAfi4jLi62q7o4H3gbcm/WhA/xzRKworqS6Owy4UlKJ8peY6yOiKU+vbHKHAt8tf3ehFfhmRPyo2JJy8R7gmuyMoR7g7QXXM6YkTh81M7OxuWvIzCxxDgIzs8Q5CMzMEucgMDNLnIPAzCxxDgKzGkgazO6UeY+kuyW9OFt+uKQbiq7P7Onw6aNmNZC0MyKmZNN/RfkajZcXXJZZXbhFYLbvpgJ9UL7B3/BzLiSdKelGST+S9H+SPpstL0n6uqRfZPfgf1+BtZvtIYkri83q4BnZFdv7U77C+ZVjbHcM5Tu/PgHcL+mLwCHAzOFnYQzfJsNsonCLwKw2j0fEMRHxHMo3ursqu7/TSD+JiB0R8UfK95aZQ/n2AnMlfVHSiUDT3RXWGpuDwGwfRcQdwAygfZTVT1RMDwKtEdEHPB+4FXgnfuCMTTDuGjLbR5KeA5SAR4DJNWw/A+iPiO9Iuh9outtKW2NzEJjVZniMAEDAkogYHL13aA8zKT+pargFfmEO9Zk9ZT591MwscR4jMDNLnIPAzCxxDgIzs8Q5CMzMEucgMDNLnIPAzCxxDgIzs8T9P3GZi2O3CoocAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_list = [10,100, 1000, 10000]\n",
    "error_list = []\n",
    "for N in N_list:\n",
    "    uniform_list = []\n",
    "    gaussian_list = []\n",
    "    third_list = []\n",
    "    \n",
    "    for a in range (0, N): #This for generate the N points for each distribution\n",
    "        uniform_list.append(rd.random())\n",
    "        new_point_gauss= gauss_generator.generate_random_point()\n",
    "        gaussian_list.append(new_point_gauss[0])\n",
    "        new_point_third =third_generator.generate_random_point()\n",
    "        third_list.append(new_point_third[0])\n",
    "    #Below, we make the binning of the generated points for each distribution\n",
    "    uniform_binned_list = np.histogram(uniform_list,bins=np.linspace(0,1,10))\n",
    "    gaussian_binned_list = np.histogram(gaussian_list,bins=np.linspace(-3,3,10))\n",
    "    third_binned_list = np.histogram(third_list,bins=np.linspace(1,7,10))\n",
    "\n",
    "    function_list = [uniform_list, gaussian_list, third_list]\n",
    "    generator_list = [0, gauss_generator, third_generator]\n",
    "    bin_f_list = [uniform_binned_list, gaussian_binned_list, third_binned_list]\n",
    "    title_list = ['Uniform','Gaussian','Third']\n",
    "   #In this loop, we compute the expected value of points for each bin, and then compare to the actual number of points in bin_f_list\n",
    "    for b in range(0,3):\n",
    "        generator = generator_list[b]\n",
    "        function = function_list[b]\n",
    "        error_n_list = []\n",
    "        for a in range(0, 9):\n",
    "            if generator == 0:\n",
    "                integral =  (bin_f_list[b][1][a+1] - bin_f_list[b][1][0]) / (bin_f_list[b][1][-1] - bin_f_list[b][1][0]) - (bin_f_list[b][1][a] - bin_f_list[b][1][0]) / (bin_f_list[b][1][-1] - bin_f_list[b][1][0])\n",
    "            else:\n",
    "                integral = generator.do_cumulative(bin_f_list[b][1][a], bin_f_list[b][1][a+1])\n",
    "            error_n_list.append((bin_f_list[b][1][a],abs(bin_f_list[b][0][a] /( integral * N) -1)))\n",
    "            plt.plot(bin_f_list[b][1][a],abs(bin_f_list[b][0][a] /( integral * N) -1), '.')\n",
    "        error_list.append(error_n_list)\n",
    "        plt.title(f'{title_list[b]}, {N} points')\n",
    "        plt.xlabel('Bins')\n",
    "        plt.ylabel('Rel Error')\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f01158ff",
   "metadata": {},
   "source": [
    "## Exercise 2\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23621e13",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\t\t\\bar{x} = \\sum_{i=1}^N \\frac{x_i}{N}, \\quad \\mathrm{e}\\quad \\bar{V} = \\sum_{i=1}^N \\frac{(x_i-\\bar{x})^2}{N},\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ddceb893",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_function(points):\n",
    "    den = len(points)\n",
    "    sum_p = [a/den for a in points]\n",
    "    return np.sum(sum_p)\n",
    "\n",
    "def var_function(points, mean):\n",
    "    den = len(points)\n",
    "    var_p = [(a - mean)**2 / den for a in points]\n",
    "    return np.sum(var_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e1962b8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The last mean was:0.003063197688933821 and the last variance was:0.8588147247037536\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_list_i= []\n",
    "var_list_i = []\n",
    "mean_list = []\n",
    "var_list = []\n",
    "for b in range(0,1000):\n",
    "    point_list = []\n",
    "    for a in range (0, 10): #This for generate the N points for each distribution\n",
    "        new_point_gauss= gauss_generator.generate_random_point()\n",
    "        point_list.append(new_point_gauss[0])\n",
    "    mean_i = mean_function(point_list)\n",
    "    var_i = var_function(point_list, mean_i)\n",
    "    mean_list_i.append(mean_i)\n",
    "    var_list_i.append(var_i)\n",
    "    mean_list.append(np.sum(mean_list_i)/ len(mean_list_i))\n",
    "    var_list.append(np.sum(var_list_i)/ len(var_list_i))\n",
    "x_list = np.linspace(1,1000,1000)\n",
    "plt.plot(x_list,mean_list, '-',color='blue',label='mean' )\n",
    "plt.plot(x_list,var_list, '-',color='red', label = 'var' )\n",
    "print(f'The last mean was:{mean_list[-1]} and the last variance was:{var_list[-1]}')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1433a246",
   "metadata": {},
   "source": [
    "The variance and the mean tend to approach more the real values of $0$ and $1$ for more calculations, although the variance estimator was not that close to the real value as the mean estimator."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f63c071",
   "metadata": {},
   "source": [
    "## Exercise 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28c681eb",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\gamma &= \\frac{1}{N\\sigma^3} \\sum_i (x_i - \\bar{x})^3, \\quad c = \\frac{1}{N\\sigma^4} \\sum_i (x_i - \\bar{x})^4 -3\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fd1f7270",
   "metadata": {},
   "outputs": [],
   "source": [
    "def skew(x, sigma, mean):\n",
    "    list_sum = []\n",
    "    for point in x:\n",
    "        list_sum.append((point - mean)**3 / (len(x) * sigma**3 ))\n",
    "    return np.sum(list_sum)\n",
    "\n",
    "def curtosis(x, sigma, mean):\n",
    "    list_sum = []\n",
    "    for point in x:\n",
    "        list_sum.append(((point - mean)**4 / (len(x) * sigma**4)))\n",
    "    return np.sum(list_sum)-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "09d44cea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8486787742833273\n",
      "2.6147880037496813\n",
      "-0.035493972545874455\n",
      "-0.2680919820091976\n",
      "0.01699045858444262\n",
      "0.22219667562621304\n",
      "0.00580161284864359\n",
      "-0.025732893368119125\n",
      "0.0011270786204663\n",
      "-0.009669092969713411\n"
     ]
    }
   ],
   "source": [
    "x_third = np.linspace(0, 10, 500)\n",
    "y_third = [third_function_pdf(a, 4, 1) for a in x_third]\n",
    "third_generator = interpolation.LinearInterp(x_third, y_third,[0,10])\n",
    "\n",
    "\n",
    "N_list = [10,100,1000,100000, 1000000]\n",
    "for N in N_list:\n",
    "    third_list = []\n",
    "    for a in range (0, N): #This for generate the N points for each distribution\n",
    "        new_point_third =third_generator.generate_random_point()\n",
    "        third_list.append(new_point_third[0])\n",
    "    mean_third = mean_function(third_list)\n",
    "    sigma = np.sqrt(var_function(third_list, mean_third))\n",
    "    print(skew(third_list, sigma, mean=mean_third))\n",
    "    print(curtosis(third_list, sigma, mean=mean_third))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3c73e1d",
   "metadata": {},
   "source": [
    "We can see that the results start to stabilize at $N=1000000$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "daa35c91",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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