Lista1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d3d55e74",
   "metadata": {},
   "outputs": [],
   "source": [
    "import nbimporter\n",
    "import tarefa1\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import math\n",
    "from pyerf import pyerf\n",
    "import scipy\n",
    "import time\n",
    "import random\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d56fa5cd",
   "metadata": {},
   "source": [
    "Interpolation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "201dfc98",
   "metadata": {},
   "outputs": [],
   "source": [
    "#gaussian\n",
    "def gaussian(mu,sigma,x):\n",
    "    fx = 1/(np.sqrt(2*np.pi)*sigma)*np.exp(-(x-mu)**2/(2*sigma**2))\n",
    "    return fx\n",
    "\n",
    "x_bins = np.linspace(-5,5,1000)\n",
    "pairs_gauss = []\n",
    "for i in range(len(x_bins)):\n",
    "    pairs_gauss.append([x_bins[i],gaussian(0,1,x_bins[i])])\n",
    "\n",
    "gauss_interpol = tarefa1.lin_interpol(pairs_gauss)\n",
    "\n",
    "\n",
    "# gauss_erf\n",
    "def gauss_erf(mu,sigma,x):\n",
    "    fx = (gaussian(mu,sigma,x)-gaussian(-mu,sigma,x)/scipy.special.erf(mu/(np.sqrt(2)*sigma)))\n",
    "    return fx\n",
    "\n",
    "\n",
    "x_bins = np.linspace(0,10,1000)\n",
    "pairs_gausserf = []\n",
    "for i in range(len(x_bins)):\n",
    "    pairs_gausserf.append([x_bins[i],gaussian(4,1,x_bins[i])])\n",
    "\n",
    "gausserf_interpol = tarefa1.lin_interpol(pairs_gausserf)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35e889e1",
   "metadata": {},
   "source": [
    "Questão 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b479ed77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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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lZmY1U8lZQ4uBYyRtA9RFxDvZl2VmZrVSyREBABHxbt+tzMxsS1PJGIGZmQ1iDgIzs4Kr5IKyYZIulnRDOr2bpOOzL83MzGqhkiOCm4B1wMYfq18G/HNmFZmZWU1VEgS7RMRV/OXK4rWAMq3KzMxqppIgWC/pQ/zlgrJdSI4Q+iRpiqSXJS2SdEEPy3eU9KikuZKel/TJflVvZmabrZIguAx4EGiSdBvwCPD1vl6U/rrZdcCxwJ7AKZL27NbsIuCuiJhEcv+iH1ReupmZVUMlF5Q9LGkOcDBJl9C5EfFWBeueDCxKL0hD0p3AVOCl0tUDI9Pno4DX+1G7mZlVQZ9BIOnfgduBmf28qGwc0FYyvRQ4qFuby4CHJX0Z2AY4ppcazgLOAthxxx37UYKZmfWlkq6hfwUOB16SdLekEyVtXaXtnwLcHBHjgU8Ct0r6QE0RMT0iWiKipbGxsUqbNjMzqCAIIuLxiPgSMAG4HjgJWF7BupcBTSXT49N5pb4A3JVu52mSn8UcW8G6zcysSiq6sjg9a+jTwBeBA4FbKnjZs8BuknaWNJRkMHhmtzavAX+TbmMPkiBor6x0MzOrhkrGCO4iGfh9ELgWeDwiuvp6XUR0SDoHeAioB2ZExHxJVwCtETETOB+4QdJ5JAPHp0dEbPrumJlZf6mvz11JnwD+IyI6a1NSeS0tLdHa2pp3GWZmWxRJcyKipadlvR4RSDo6In5DcjbPVOn9FxNHxL1VrdLMzHJRrmvoCOA3wN/2sCwAB4GZ2SDQaxBExKXp0ysi4pXSZZJ2zrQqMzOrmUrOGrqnh3l3V7sQMzPLR7kxgt2BvYBRkv6uZNFIktM8zcxsECg3RvAR4HhgNO8fJ3gHODPDmszMrIbKjRHcB9wn6ZD0ql8zMxuE+rygDJgr6WySbqL/6hKKiM9nVpWZmdVMJYPFtwLbA58AHie5Z9A7WRZlZma1U0kQ7BoRFwPvRsQtwHF88HbSZma2haokCDakf1dJ2pvkB2Q+nF1JZmZWS5WMEUyXNAa4mOTuocOBSzKtyszMaqaSn6q8MX36OMlvEpiZ2SBS7oKyr5R7YURcXf1yzMys1sodEYyoWRVmZpabcheUXV7LQszMLB99njUkaaKkRyS9mE7vK+mi7EszM7NaqOT00RuAC0lPI42I50l+f9jMzAaBSoJgWEQ8021eRxbFmJlZ7VUSBG9J2oXkV8mQdCLwx0pWLmmKpJclLZJ0QS9tTpL0kqT5km6vuHIzM6uKSi4oOxuYDuwuaRnwCnBqXy+SVA9cB3wMWAo8K2lmRLxU0mY3km6nwyJipSRfsWxmVmOVXFC2GDhG0jYkRxBrScYIXu3jpZOBRenrkXQnMBV4qaTNmcB1EbEy3dbyfu+BmZltll67hiSNlHShpGslfYwkAKYBi4CTKlj3OKCtZHppOq/URGCipN9JmiVpSi+1nCWpVVJre3t7BZs2M7NKlTsiuBVYCTxN8s39m4CAT0XEvCpufzfgSJLbWz8haZ+IWFXaKCKmk3RP0dLSElXatpmZUT4IJkTEPgCSbiQZIN4xIt6rcN3LgKaS6fHpvFJLgdkRsQF4RdJCkmB4tsJtmJnZZip31tDG208TEZ3A0n6EACQf5rtJ2lnSUJJxhZnd2vyC5GgASWNJuooW92MbZma2mcodEewn6e30uYAPpdMCIiJGlltxRHRIOgd4CKgHZkTEfElXAK0RMTNd9nFJLwGdwNciYsVm7pOZmfWDIrasLveWlpZobW3Nuwwzsy2KpDkR0dLTskouKDMzs0HMQWBmVnAOAjOzgnMQmJkVnIPAzKzgHARmZgXnIDAzKzgHgZlZwTkIzMwKzkFgZlZwDgIzs4JzEJiZFZyDwMys4BwEZmYF5yAwMys4B4GZWcE5CMzMCs5BYGZWcA4CM7OCyzQIJE2R9LKkRZIuKNPu05JCUo+/p2lmZtnJLAgk1QPXAccCewKnSNqzh3YjgHOB2VnVYmZmvcvyiGAysCgiFkfEeuBOYGoP7a4Evg28l2EtZmbWiyyDYBzQVjK9NJ33XyQdADRFxK8yrMPMzMrIbbBYUh1wNXB+BW3PktQqqbW9vT374szMCiTLIFgGNJVMj0/nbTQC2Bt4TNIS4GBgZk8DxhExPSJaIqKlsbExw5LNzIonyyB4FthN0s6ShgInAzM3LoyI1RExNiKaI6IZmAWcEBGtGdZkZmbdZBYEEdEBnAM8BCwA7oqI+ZKukHRCVts1M7P+achy5RFxP3B/t3mX9NL2yCxrMTOznvnKYjOzgnMQmJkVnIPAzKzgHARmA8jrCxcw++d38frCBXmXYgWS6WCxmVXu9YUL+NmV36Szo4P6hgY+c/G32GHiHnmXZQXgIwKzAaJt/gt0dnQQXV10dnTQNv+FvEuygnAQmA0QTXvtQ31DA6qro76hgaa99sm7JCsIdw2ZDRA7TNyDz1z8Ldrmv0DTXvu4W8hqxkFgNoDsMHEPB4DVnLuGzMwKzkFgZlZwDgIzs4JzEJjZgNTW1saTTz5JW1tb341ts3iw2MwGnLa2Nm655RY6Ozupr69n2rRpNDU19f1C2yQ+IjCzAWfJkiV0dnYSEXR2drJkyZK8SxrUHARmNuA0NzdTX1+PJOrr62lubs67pEHNXUNmNuA0NTUxbdo0lixZQnNzs7uFMuYgMLMBqampyQFQI+4aMjMrOAeBmVnBZRoEkqZIelnSIkkX9LD8K5JekvS8pEck7ZRlPWZm9kGZBYGkeuA64FhgT+AUSXt2azYXaImIfYG7gauyqsfMzHqW5RHBZGBRRCyOiPXAncDU0gYR8WhErE0nZwHjM6zHzMx6kGUQjANKrw1fms7rzReAB3paIOksSa2SWtvb26tYopmZDYjBYkmfBVqA7/S0PCKmR0RLRLQ0NjbWtjgzs0Euy+sIlgGlJwGPT+e9j6RjgG8CR0TEugzrMTOzHmR5RPAssJuknSUNBU4GZpY2kDQJuB44ISKWZ1iLmZn1IrMgiIgO4BzgIWABcFdEzJd0haQT0mbfAYYDP5M0T9LMXlZnZmYZyfQWExFxP3B/t3mXlDw/Jsvtm5lZ3wbEYLGZmeXHQWBmVnAOAjOzgnMQmJkVnIPADHhj8WrmPLiENxavzrsUs5rzD9NY4b2xeDX3/d+5dHZ0Ud9Qx9TzJrH9hFF5l2VWMz4isMJbtnAlnR1dREBnZxfLFq7MuySzmnIQWOGNmziG+oY6VAf19XWMmzgm75LMaspdQ1Z4208YxdTzJrFs4UrGTRzjbiErHAeBGUkYOACsqNw1ZGZWcA4CM7OCcxCYmRWcg8DMrOAcBGZmBecgMDMrOEVE3jX0i6R24NW868jIWOCtvIvI0GDfPxj8++j923LtFBGNPS3Y4oJgMJPUGhEtedeRlcG+fzD499H7Nzi5a8jMrOAcBGZmBecgGFim511Axgb7/sHg30fv3yDkMQIzs4LzEYGZWcE5CMzMCs5BkDNJTZIelfSSpPmSzs27pmqTtLWkZyT9Pt3Hy/OuKQuS6iXNlfTLvGvJgqQlkl6QNE9Sa971VJuk0ZLulvQHSQskHZJ3TbXi3yPIXwdwfkQ8J2kEMEfSryPipbwLq6J1wNERsUbSEOC3kh6IiFl5F1Zl5wILgJF5F5KhoyJisF5wdQ3wYEScKGkoMCzvgmrFRwQ5i4g/RsRz6fN3SD5IxuVbVXVFYk06OSR9DKqzFCSNB44Dbsy7Fus/SaOAjwL/BhAR6yNiVa5F1ZCDYACR1AxMAmbnXErVpd0m84DlwK8jYrDt43eBrwNdOdeRpQAeljRH0ll5F1NlOwPtwE1p996NkrbJu6hacRAMEJKGA/cA/zsi3s67nmqLiM6I2B8YD0yWtHfOJVWNpOOB5RExJ+9aMvbXEXEAcCxwtqSP5l1QFTUABwA/jIhJwLvABfmWVDsOggEg7Te/B7gtIu7Nu54spYfbjwJTci6lmg4DTpC0BLgTOFrST/ItqfoiYln6dznwc2ByvhVV1VJgacmR6t0kwVAIDoKcSRJJv+SCiLg673qyIKlR0uj0+YeAjwF/yLWoKoqICyNifEQ0AycDv4mIz+ZcVlVJ2iY9mYG0y+TjwIv5VlU9EfEG0CbpI+msvwEG0wkbZfmsofwdBpwGvJD2oQP8U0Tcn19JVfdXwC2S6km+fNwVEYPyFMtBbDvg58n3FhqA2yPiwXxLqrovA7elZwwtBj6Xcz0141tMmJkVnLuGzMwKzkFgZlZwDgIzs4JzEJiZFZyDwMys4BwEZhWQ1JnedfP3kp6TdGg6fwdJd+ddn9nm8OmjZhWQtCYihqfPP0FyrccROZdlVhU+IjDrv5HASkhuFCjpxfT56ZLulfSgpP+UdFU6v17SzZJeTO/nf16OtZt9gK8sNqvMh9Irv7cmuVL66F7a7U9yB9l1wMuSvg98GBgXEXtD8gMoWRdr1h8+IjCrzJ8jYv+I2J3khnk/Tu8T1d0jEbE6It4juVfNTiS3K5gg6fuSpgCD7u6ytmVzEJj1U0Q8DYwFGntYvK7keSfQEBErgf2Ax4Av4h+vsQHGXUNm/SRpd6AeWEEFP2coaSywPiLukfQyMOhuUW1bNgeBWWU2jhEACJgWEZ099w59wDiSX77aeAR+YQb1mW0ynz5qZlZwHiMwMys4B4GZWcE5CMzMCs5BYGZWcA4CM7OCcxCYmRWcg8DMrOD+P6kn0MPdtr1rAAAAAElFTkSuQmCC\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"
    },
    {
     "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_size = [10,100,1000,10000]\n",
    "bins = 10\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "for N in N_size:\n",
    "#letra a\n",
    "    \n",
    "    #uniform\n",
    "    uniform_sample = np.random.uniform(0,1,N)\n",
    "    \n",
    "    #gaussian\n",
    "    sampler_gaussiano = tarefa1.sampler(pairs_gauss)\n",
    "    gaussian_sample = sampler_gaussiano.sample(N)\n",
    "    \n",
    "    #gaussian_erf\n",
    "    sampler_gausserf = tarefa1.sampler(pairs_gausserf)\n",
    "    gaussianerf_sample = sampler_gausserf.sample(N)\n",
    "\n",
    "#letra b\n",
    "    \n",
    "    #uniform\n",
    "    binned_uniform = np.histogram(uniform_sample, bins, range = (0,1))\n",
    "    n_uniform = []\n",
    "    for i in range(len(binned_uniform[1])-1):\n",
    "        n_uniform.append((binned_uniform[1][i+1]-binned_uniform[1][i])*N)\n",
    "    \n",
    "    n_uniform_error = abs(binned_uniform[0]-n_uniform)/n_uniform\n",
    "    \n",
    "    \n",
    "    #gaussian\n",
    "    binned_gaussian = np.histogram(gaussian_sample, bins, range = (-3,3))\n",
    "    n_gaussian = []\n",
    "    for i in range(len(binned_gaussian[1])-1):\n",
    "        n_gaussian.append(N*gauss_interpol.integral(binned_gaussian[1][i],binned_gaussian[1][i+1]))\n",
    "    \n",
    "    n_gaussian_error = abs(binned_gaussian[0]-n_gaussian)/n_gaussian\n",
    "    \n",
    "    \n",
    "    #gaussian_erf\n",
    "    binned_gaussianerf = np.histogram(gaussianerf_sample, bins, range = (1,7))\n",
    "    n_gaussianerf = []\n",
    "    for i in range(len(binned_gaussianerf[1])-1):\n",
    "        n_gaussianerf.append(N*gausserf_interpol.integral(binned_gaussianerf[1][i],binned_gaussianerf[1][i+1]))\n",
    "    \n",
    "    n_gaussianerf_error = abs(binned_gaussianerf[0]-n_gaussianerf)/n_gaussianerf\n",
    "    \n",
    "    \n",
    "#letra c\n",
    "    \n",
    "    #uniform\n",
    "    for i in range(len(binned_uniform[1])-1):\n",
    "        plt.plot((binned_uniform[1][i+1]+binned_uniform[1][i])/2, n_uniform_error[i],'.')\n",
    "    plt.xlabel('Bins')\n",
    "    plt.ylabel('Relative error')\n",
    "    plt.title('Uniform, '+ str(N) + ' points')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    #gaussian\n",
    "    for i in range(len(binned_gaussian[1])-1):\n",
    "        plt.plot((binned_gaussian[1][i+1]+binned_gaussian[1][i])/2, n_gaussian_error[i],'.')\n",
    "    plt.xlabel('Bins')\n",
    "    plt.ylabel('Relative error')\n",
    "    plt.title('Gaussian, '+ str(N) + ' points')\n",
    "    plt.show()\n",
    "    \n",
    "    #gaussian_erf\n",
    "    for i in range(len(binned_gaussianerf[1])-1):\n",
    "        plt.plot((binned_gaussianerf[1][i+1]+binned_gaussianerf[1][i])/2, n_gaussianerf_error[i],'.')\n",
    "    plt.xlabel('Bins')\n",
    "    plt.ylabel('Relative error')\n",
    "    plt.title('Gaussian_erf, '+ str(N) + ' points')\n",
    "    plt.show()\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32d4a416",
   "metadata": {},
   "source": [
    "Questão 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2c6dfbb2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean_mean = 0.011612705042571031\n",
      "Variance_mean = 1.0030297489036308\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": [
    "gaussian_sample = []\n",
    "mean_mean = []\n",
    "variance_mean = []\n",
    "mean = []\n",
    "variance = []\n",
    "t_list = []\n",
    "for t in range(1,1000):\n",
    "    gaussian_sample = []\n",
    "    for N in range(0,11):\n",
    "        gaussian_sample.append(random.gauss(0,1))\n",
    "    \n",
    "    \n",
    "    mean.append(np.sum(gaussian_sample)/N)\n",
    "    variance.append(np.sum((mean[t-1] - gaussian_sample)**2)/N)\n",
    "    \n",
    "    mean_mean.append(np.sum(mean)/t)\n",
    "    variance_mean.append(np.sum(variance)/t)\n",
    "    t_list.append(t)\n",
    "\n",
    "    \n",
    "\n",
    "plt.plot(t_list,mean_mean, label = 'Mean mean')\n",
    "plt.plot(t_list,variance_mean, label = 'Variance mean')\n",
    "plt.legend()\n",
    "print('Mean_mean = ' + str(mean_mean[-1]))\n",
    "print('Variance_mean = ' +  str(variance_mean[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9bf096e",
   "metadata": {},
   "source": [
    "Questão 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "70bf0aba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Skew hasn't stabilized yet.\n",
      "0.01607139285999757\n",
      "Curtosis hasn't stabilized yet.\n",
      "-0.012926170415946903\n"
     ]
    }
   ],
   "source": [
    "N_size = [10,100,1000,10000,100000]\n",
    "skew = []\n",
    "curtosis = []\n",
    "sampler_gausserf = tarefa1.sampler(pairs_gausserf)\n",
    "\n",
    "for N in N_size:\n",
    "    gaussianerf_sample = sampler_gausserf.sample(N)\n",
    "    mean = np.sum(gaussianerf_sample)/N\n",
    "    std = np.sqrt((np.sum((mean - gaussianerf_sample)**2)/N))\n",
    "    \n",
    "    skew.append(np.sum((gaussianerf_sample - mean)**3)/(N*std**3))\n",
    "    curtosis.append(np.sum((gaussianerf_sample - mean)**4)/(N*std**4)-3)\n",
    "    \n",
    "\n",
    "for i in range(len(skew)):\n",
    "    if abs(skew[i]) < 0.01:\n",
    "        print('skew stabilized in N = ' + str(N_size[i]))\n",
    "        print(skew[i])\n",
    "        break\n",
    "    if i == len(skew)-1:\n",
    "        print(\"Skew hasn't stabilized yet.\")\n",
    "        print(skew[i])\n",
    "    \n",
    "\n",
    "for i in range(len(curtosis)):\n",
    "    if abs(curtosis[i]) < 0.01:\n",
    "        print('curtosis stabilized in N = ' + str(N_size[i]))\n",
    "        print(curtosis[i])\n",
    "        break\n",
    "    if i == len(curtosis)-1:\n",
    "        print(\"Curtosis hasn't stabilized yet.\")\n",
    "        print(curtosis[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "123f4ab1",
   "metadata": {},
   "source": [
    "Questão 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cfdff469",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr(xi,yi) = -0.01821523939329417\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr(xi,yi+xi) = 0.2612473222973975\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr(xi,yi-xi) = -0.29355361103895755\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": [
    "sampler_gausserf = tarefa1.sampler(pairs_gausserf)\n",
    "N_size = np.linspace(10,10000,10,dtype = int)\n",
    "cov_a = []\n",
    "corr_a = []\n",
    "cov_plus = []\n",
    "corr_plus = []\n",
    "cov_minus = []\n",
    "corr_minus = []\n",
    "\n",
    "\n",
    "for N in N_size:\n",
    "#letra a \n",
    "    uniform_sample = np.random.uniform(0,1,N)\n",
    "    uniform_mean = np.sum(uniform_sample)/N\n",
    "    uniform_std = np.sqrt((np.sum((uniform_mean - uniform_sample)**2)/N))\n",
    "    \n",
    "    gaussian_sample = sampler_gaussiano.sample(N)\n",
    "    gaussian_mean = np.sum(gaussian_sample)/N\n",
    "    gaussian_std = np.sqrt((np.sum((gaussian_sample - gaussian_mean)**2)/N))\n",
    "    \n",
    "    cov_a.append(np.sum((uniform_sample-uniform_mean)*(gaussian_sample-gaussian_mean))/N)\n",
    "    corr_a.append((np.sum((uniform_sample-uniform_mean)*(gaussian_sample-gaussian_mean))/N)/(uniform_std*gaussian_std))\n",
    "\n",
    "#letra b\n",
    "    gaussian_plus_sample = gaussian_sample+uniform_sample\n",
    "    gaussian_plus_mean = np.sum(gaussian_plus_sample)/N\n",
    "    gaussian_plus_std = np.sqrt((np.sum((gaussian_plus_sample - gaussian_plus_mean)**2)/N))\n",
    "    \n",
    "    cov_plus.append(np.sum((uniform_sample-uniform_mean)*(gaussian_plus_sample-gaussian_plus_mean))/N)\n",
    "    corr_plus.append((np.sum((uniform_sample-uniform_mean)*(gaussian_plus_sample-gaussian_plus_mean))/N)/(uniform_std*gaussian_plus_std))\n",
    "    \n",
    "    \n",
    "    gaussian_minus_sample = gaussian_sample - uniform_sample\n",
    "    gaussian_minus_mean = np.sum(gaussian_minus_sample)/N\n",
    "    gaussian_minus_std = np.sqrt((np.sum((gaussian_minus_sample - gaussian_minus_mean)**2)/N))\n",
    "    \n",
    "    cov_minus.append(np.sum((uniform_sample-uniform_mean)*(gaussian_minus_sample-gaussian_minus_mean))/N)\n",
    "    corr_minus.append((np.sum((uniform_sample-uniform_mean)*(gaussian_minus_sample-gaussian_minus_mean))/N)/(uniform_std*gaussian_minus_std))\n",
    " \n",
    "\n",
    "\n",
    "#letra c\n",
    "plt.scatter(uniform_sample,gaussian_sample)\n",
    "plt.ylabel('yi')\n",
    "plt.xlabel('xi')\n",
    "plt.show()\n",
    "print('Corr(xi,yi) = ' +str(corr_a[-1]))\n",
    "\n",
    "plt.scatter(uniform_sample,gaussian_plus_sample)\n",
    "plt.ylabel('yi+xi')\n",
    "plt.xlabel('xi')\n",
    "plt.show()\n",
    "print('Corr(xi,yi+xi) = ' +str(corr_plus[-1]))\n",
    "\n",
    "plt.scatter(uniform_sample,gaussian_minus_sample)\n",
    "plt.ylabel('yi-xi')\n",
    "plt.xlabel('xi')\n",
    "plt.show()\n",
    "print('Corr(xi,yi-xi) = ' +str(corr_minus[-1]))\n",
    "\n",
    "plt.scatter(uniform_sample,uniform_sample)\n",
    "plt.ylabel('xi')\n",
    "plt.xlabel('xi')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de847d68",
   "metadata": {},
   "source": [
    "Questão 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1d61d4f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwhlqSCmeoJalwVYU6ImZGxJMR8VREXF7voSRJf9JrqCOiCfhn4APA0cCHIuLoeg8mSepWzRb1VOCpzHw6M/8IfA+YU9+xJEnbRGbufoGIvwJmZub5lctnA8dl5gU7LTcfmF+5eBTwZD9nOhjY0M/7ls51G7qG8/q5bmV4Z2a29nTDiFo9Q2beBNw00MeJiOWZ2VmDkYrjug1dw3n9XLfyVbPr4zngHTtcbqtcJ0kaBNWE+r+AIyNiXETsDXwQuLO+Y0mStul110dmbomIC4B7gCbgG5m5po4zDXj3ScFct6FrOK+f61a4Xl9MlCQ1lu9MlKTCGWpJKlxRoY6Ipoh4NCLuavQstRYRB0bEbRHxREQ8HhHTGj1TrUTE30bEmohYHRGLIqKl0TMNRER8IyJejIjVO1z3toi4NyLWVf48qJEz9tcu1u26yt/LVRFxe0Qc2MAR+62nddvhtk9GREbEwY2YbaCKCjVwEfB4o4eoky8DP87MdwGTGCbrGRGHAxcCnZnZQfcLzh9s7FQDdgswc6frLgd+lplHAj+rXB6KbuGt63Yv0JGZE4H/Bq4Y7KFq5Bbeum5ExDuAU4FfD/ZAtVJMqCOiDZgFfK3Rs9RaRBwAvAf4OkBm/jEzf9vQoWprBLBPRIwARgHPN3ieAcnMB4CXd7p6DrCw8v1CYO5gzlQrPa1bZv4kM7dULj5M93slhpxd/HcD+EfgUmDIHjlRTKiBG+j+Yf5fg+eoh3HAS8A3K7t2vhYR+zZ6qFrIzOeAL9K9tfICsCkzf9LYqeri7Zn5QuX73wBvb+QwdfRR4O5GD1ErETEHeC4zH2v0LANRRKgj4nTgxcxc0ehZ6mQE8G7gXzJzCvAaQ/dX5zep7KudQ/c/RocB+0bERxo7VX1l9zGtQ3brbFci4u+ALcCtjZ6lFiJiFHAl8NlGzzJQRYQaOBGYHRHr6T4734yI+E5jR6qpLqArM5dVLt9Gd7iHg/cB/5OZL2XmG8APgRMaPFM9/G9EHApQ+fPFBs9TUxFxLnA6cFYOnzdX/DndGxCPVdrSBvwiIg5p6FT9UESoM/OKzGzLzHa6X4i6LzOHzVZZZv4GeDYijqpcdQqwtoEj1dKvgeMjYlREBN3rNixeKN3JncC8yvfzgH9v4Cw1FREz6d7tODszf9/oeWolM3+ZmX+Wme2VtnQB7678/zikFBHqPcQngFsjYhUwGbi6sePURuW3hNuAXwC/pPvv1JB+225ELAIeAo6KiK6IOA+4Bnh/RKyj+7eIaxo5Y3/tYt2+CuwH3BsRKyNiQUOH7KddrNuw4FvIJalwblFLUuEMtSQVzlBLUuEMtSQVzlBLUuEMtSQVzlBLUuH+Hzn+807fbslbAAAAAElFTkSuQmCC\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": [
    "def binomial_sample(n):\n",
    "    success = 0\n",
    "    lamb = 9\n",
    "    p = lamb/n\n",
    "    uniform_sample = np.random.uniform(0,1,n)\n",
    "    for toss in uniform_sample:\n",
    "        if toss <= p:\n",
    "            success +=1\n",
    "    return success\n",
    "\n",
    "N_size = [10,100,1000,10000]\n",
    "for N in N_size:\n",
    "    binomial = []\n",
    "    for i in range(0,N):\n",
    "        binomial.append(binomial_sample(N))\n",
    "    \n",
    "    poisson_sample = np.random.poisson(9,N)\n",
    "    plt.hist(poisson_sample,label = 'Poisson')\n",
    "    plt.hist(binomial, label = 'Binomial')\n",
    "    plt.title('N = '+str(N))\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d581b593",
   "metadata": {},
   "source": [
    "Questão 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5231b195",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "lamb_list = [1,5,20,100,1000,10000]\n",
    "for lamb in lamb_list:\n",
    "    poisson_sample = np.random.poisson(lamb,100000)\n",
    "    x_list = np.linspace(lamb-3*np.sqrt(lamb),lamb+3*np.sqrt(lamb),1000)\n",
    "    gaussianpdf = [gaussian(lamb,np.sqrt(lamb),x) for x in x_list]\n",
    "    plt.hist(poisson_sample,density = True,bins = 100)\n",
    "    plt.plot(x_list,gaussianpdf)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92b9c38c",
   "metadata": {},
   "source": [
    "Questão 7"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ec6a5dd",
   "metadata": {},
   "source": [
    "$P(n \\sigma) = \\int_{\\Omega_n}P(x,y)dxdy$\n",
    "\n",
    "$P(x,y) = \\frac{e^{-\\frac{1}{2} \\left ( \\frac{x-\\mu_x}{\\sigma_x}  \\right )^2 - \\frac{1}{2} \\left ( \\frac{y-\\mu_y}{\\sigma_y}  \\right )^2}}{2\\pi \\sigma_x \\sigma_y} $\n",
    "\n",
    "making the transformation \n",
    "\n",
    "$x' =  \\left (\\frac{x-\\mu_x}{\\sigma_x}  \\right) , y' = \\left (\\frac{y-\\mu_y}{\\sigma_y}  \\right)$ we got\n",
    "\n",
    "$P(n \\sigma) = \\frac{1}{2\\pi}\\int_{\\Omega_n}e^{-\\frac{x'^2+y'^2}{2}}dx'dy'$\n",
    "\n",
    "now going to polar cordinates we got\n",
    "\n",
    "$P(n \\sigma) =\\frac{1}{2\\pi} \\int_{0}^{\\chi} \\int_{0}^{2\\pi} e^{-\\frac{r^2}{2}}r d\\theta dr = 1 - e^{-\\frac{\\chi^2}{2}} $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4de964ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 1 então P(n*sigma) = 0.3934693402873666\n",
      "n = 2 então P(n*sigma) = 0.8646647167633873\n",
      "n = 3 então P(n*sigma) = 0.9888910034617577\n",
      "n = 4 então P(n*sigma) = 0.9996645373720975\n",
      "n = 5 então P(n*sigma) = 0.999996273346828\n",
      "n = 6 então P(n*sigma) = 0.9999999847700203\n",
      "n = 7 então P(n*sigma) = 0.9999999999771026\n",
      "n = 8 então P(n*sigma) = 0.9999999999999873\n",
      "n = 9 então P(n*sigma) = 1.0\n"
     ]
    }
   ],
   "source": [
    "for chi in range(1,10):\n",
    "    print(\"n = \"+ str(chi) + ' então P(n*sigma) = '+ str(1-np.exp(-chi**2/2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7858dab0",
   "metadata": {},
   "source": [
    "Questão 8"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf1d9556",
   "metadata": {},
   "source": [
    "Repeating the procedure above for the new distribution we get\n",
    "\n",
    "\n",
    "$P(n \\sigma) =\\frac{1}{2\\pi} \\int_{0}^{\\chi} \\int_{0}^{2\\pi} e^{-\\frac{r^2}{2}}r d\\theta dr = 1 - e^{-\\frac{\\chi^2}{2(1-\\rho^2)}} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6e4e9e4b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 1 então P(n*sigma) = 0.486582880967408\n",
      "n = 2 então P(n*sigma) = 0.9305165487771985\n",
      "n = 3 então P(n*sigma) = 0.9975212478233336\n",
      "n = 4 então P(n*sigma) = 0.9999766908988571\n",
      "n = 5 então P(n*sigma) = 0.9999999422225148\n",
      "n = 6 então P(n*sigma) = 0.9999999999622486\n",
      "n = 7 então P(n*sigma) = 0.9999999999999934\n",
      "n = 8 então P(n*sigma) = 1.0\n",
      "n = 9 então P(n*sigma) = 1.0\n"
     ]
    }
   ],
   "source": [
    "rho = 0.5\n",
    "for chi in range(1,10):\n",
    "    print(\"n = \"+ str(chi) + ' então P(n*sigma) = '+ str(1-(np.exp(-chi**2/2/(1-rho**2)))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b228b14",
   "metadata": {},
   "source": [
    "Questão 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cf9ad3e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform case\n",
      "real mean = 0.5\n",
      "arithimetic mean = 0.5072671928910253\n",
      "10 first = 0.4989502029276883\n",
      "arithimetic -1 = 0.5077744600839162\n",
      "1.8 = 1.8\n",
      "geometric = 0.0\n",
      "mode = 0.049876644203182274\n",
      "max_min_2 = 0.49917307631199276\n",
      "only even = 0.5089902921452256\n",
      "\n",
      " Gaussian case\n",
      "real mean = 0\n",
      "arithimetic mean = 0.0321330128044877\n",
      "10 first = -0.5814038614918084\n",
      "arithimetic -1 = 0.03216517798247017\n",
      "1.8 = 1.8\n",
      "geometric = 0.5524799749664044\n",
      "mode = -1.22394232765282\n",
      "max_min_2 = -0.031245621389341727\n",
      "only even = 0.03305446419836839\n",
      "\n",
      " Gaussian_erf case\n",
      "real mean = 4\n",
      "arithimetic mean = 3.901571025165154\n",
      "10 first = 4.958320595428276\n",
      "arithimetic -1 = 3.9409808335001557\n",
      "1.8 = 1.8\n",
      "geometric = 3.6962731882348634\n",
      "mode = 4.087526230034882\n",
      "max_min_2 = 3.6163297892458868\n",
      "only even = 3.8492955081854374\n"
     ]
    }
   ],
   "source": [
    "#letra a\n",
    "\n",
    "#uniform\n",
    "uniform_sample = [np.random.uniform(0,1) for i in range(0,1001)]\n",
    "uniform_estimators = tarefa1.mean_estimators(uniform_sample)\n",
    "\n",
    "print('Uniform case')\n",
    "print('real mean = ' + str(0.5))\n",
    "print('arithimetic mean = ' + str(uniform_estimators.arithimetic()))\n",
    "print('10 first = ' + str(uniform_estimators.ten_first()))\n",
    "print('arithimetic -1 = ' + str(uniform_estimators.arithimetic_1()))\n",
    "print('1.8 = ' + str(uniform_estimators.one_eight()))\n",
    "print('geometric = ' + str(uniform_estimators.geometric()))\n",
    "print('mode = ' + str(uniform_estimators.mode()))\n",
    "print('max_min_2 = ' + str(uniform_estimators.max_min_mean()))\n",
    "print('only even = '+ str(uniform_estimators.only_even()))\n",
    "\n",
    "\n",
    "#gaussian\n",
    "sampler_gaussiano = tarefa1.sampler(pairs_gauss)\n",
    "gaussian_sample = sampler_gaussiano.sample(1000)\n",
    "gaussian_estimators = tarefa1.mean_estimators(gaussian_sample)\n",
    "\n",
    "print('\\n Gaussian case')\n",
    "print('real mean = ' + str(0))\n",
    "print('arithimetic mean = ' + str(gaussian_estimators.arithimetic()))\n",
    "print('10 first = ' + str(gaussian_estimators.ten_first()))\n",
    "print('arithimetic -1 = ' + str(gaussian_estimators.arithimetic_1()))\n",
    "print('1.8 = ' + str(gaussian_estimators.one_eight()))\n",
    "print('geometric = ' + str(gaussian_estimators.geometric()))\n",
    "print('mode = ' + str(gaussian_estimators.mode()))\n",
    "print('max_min_2 = ' + str(gaussian_estimators.max_min_mean()))\n",
    "print('only even = '+ str(gaussian_estimators.only_even()))\n",
    "    \n",
    "#gaussian_erf\n",
    "sampler_gausserf = tarefa1.sampler(pairs_gausserf)\n",
    "gaussianerf_sample = sampler_gausserf.sample(100)\n",
    "gaussianerf_estimators = tarefa1.mean_estimators(gaussianerf_sample)\n",
    "\n",
    "print('\\n Gaussian_erf case')\n",
    "print('real mean = ' + str(4))\n",
    "print('arithimetic mean = ' + str(gaussianerf_estimators.arithimetic()))\n",
    "print('10 first = ' + str(gaussianerf_estimators.ten_first()))\n",
    "print('arithimetic -1 = ' + str(gaussianerf_estimators.arithimetic_1()))\n",
    "print('1.8 = ' + str(gaussianerf_estimators.one_eight()))\n",
    "print('geometric = ' + str(gaussianerf_estimators.geometric()))\n",
    "print('mode = ' + str(gaussianerf_estimators.mode()))\n",
    "print('max_min_2 = ' + str(gaussianerf_estimators.max_min_mean()))\n",
    "print('only even = '+ str(gaussianerf_estimators.only_even()))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d33f9967",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Consistency test for 100000 points in the sample. \n",
      "\n",
      "Uniform case\n",
      "real mean = 0.5\n",
      "arithimetic mean consistency =  0.0013380417429293967\n",
      "10 first = 0.10124631630791775\n",
      "arithimetic -1 = 0.0013430551734811003\n",
      "1.8 = 1.3\n",
      "geometric = -0.5\n",
      "mode = -0.07696067063688206\n",
      "max_min_2 = 5.697920357761177e-09\n",
      "only even = 0.001055931472634275\n",
      "\n",
      " Gaussian case\n",
      "real mean = 0\n",
      "arithimetic mean consistency =  0.1471320257344422\n",
      "10 first = 0.5711454938054951\n",
      "arithimetic -1 = 0.14861820781256788\n",
      "1.8 = 1.8\n",
      "geometric = nan\n",
      "mode = 0.7768224935745622\n",
      "max_min_2 = 0.22339856980956685\n",
      "only even = 0.002605373994847331\n",
      "\n",
      " Gaussian_erf case\n",
      "real mean = 0\n",
      "arithimetic mean consistency =  0.06614215831925918\n",
      "10 first = 0.5274400140860962\n",
      "arithimetic -1 = 0.10721430133258458\n",
      "1.8 = 2.2\n",
      "geometric = 0.0540375945691145\n",
      "mode = 0.5649836214800459\n",
      "max_min_2 = 0.4931918119167644\n",
      "only even = 0.25418373658639926\n",
      "\n",
      " Bias test for the estimators. \n",
      " \n"
     ]
    }
   ],
   "source": [
    "#letra b\n",
    "\n",
    "print('Consistency test for 100000 points in the sample. \\n')\n",
    "#consitency\n",
    "\n",
    "#uniform sample\n",
    "uniform_sample = [np.random.uniform(0,1) for i in range(0,100000)]\n",
    "uniform_estimators = tarefa1.mean_estimators(uniform_sample)\n",
    "\n",
    "print('Uniform case')\n",
    "print('real mean = ' + str(0.5))\n",
    "print('arithimetic mean consistency =  ' + str(abs(uniform_estimators.arithimetic()-0.5)))\n",
    "print('10 first = ' + str(abs(uniform_estimators.ten_first()-0.5)))\n",
    "print('arithimetic -1 = ' + str(abs(uniform_estimators.arithimetic_1()-0.5)))\n",
    "print('1.8 = ' + str(abs(uniform_estimators.one_eight()-0.5)))\n",
    "print('geometric = ' + str(abs(uniform_estimators.geometric())-0.5))\n",
    "print('mode = ' + str(abs(uniform_estimators.mode())-0.5))\n",
    "print('max_min_2 = ' + str(abs(uniform_estimators.max_min_mean()-0.5)))\n",
    "print('only even = '+ str(abs(uniform_estimators.only_even()-0.5)))\n",
    "\n",
    "#gaussian sample\n",
    "sampler_gaussiano = tarefa1.sampler(pairs_gauss)\n",
    "gaussian_sample = sampler_gaussiano.sample(100000)\n",
    "gaussian_estimators = tarefa1.mean_estimators(gaussian_sample)\n",
    "\n",
    "print('\\n Gaussian case')\n",
    "print('real mean = ' + str(0))\n",
    "print('arithimetic mean consistency =  ' + str(abs(gaussian_estimators.arithimetic()-0)))\n",
    "print('10 first = ' + str(abs(gaussian_estimators.ten_first()-0)))\n",
    "print('arithimetic -1 = ' + str(abs(gaussian_estimators.arithimetic_1()-0)))\n",
    "print('1.8 = ' + str(abs(gaussian_estimators.one_eight()-0)))\n",
    "print('geometric = ' + str(abs(gaussian_estimators.geometric()-0)))\n",
    "print('mode = ' + str(abs(gaussian_estimators.mode()-0)))\n",
    "print('max_min_2 = ' + str(abs(gaussian_estimators.max_min_mean()-0)))\n",
    "print('only even = '+ str(abs(gaussian_estimators.only_even()-0)))\n",
    "\n",
    "\n",
    "#gaussian_erf sample\n",
    "sampler_gausserf = tarefa1.sampler(pairs_gausserf)\n",
    "gaussianerf_sample = sampler_gausserf.sample(100000)\n",
    "gaussianerf_estimators = tarefa1.mean_estimators(gaussianerf_sample)\n",
    "\n",
    "print('\\n Gaussian_erf case')\n",
    "print('real mean = ' + str(0))\n",
    "print('arithimetic mean consistency =  ' + str(abs(gaussianerf_estimators.arithimetic()-4)))\n",
    "print('10 first = ' + str(abs(gaussianerf_estimators.ten_first()-4)))\n",
    "print('arithimetic -1 = ' + str(abs(gaussianerf_estimators.arithimetic_1()-4)))\n",
    "print('1.8 = ' + str(abs(gaussianerf_estimators.one_eight()-4)))\n",
    "print('geometric = ' + str(abs(gaussianerf_estimators.geometric()-4)))\n",
    "print('mode = ' + str(abs(gaussianerf_estimators.mode()-4)))\n",
    "print('max_min_2 = ' + str(abs(gaussianerf_estimators.max_min_mean()-4)))\n",
    "print('only even = '+ str(abs(gaussianerf_estimators.only_even()-4)))\n",
    "\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "89f18f83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bias test for the estimators for size 20 sample with 10 realizations. \n",
      " \n",
      "Uniform case\n",
      "real mean = 0.5\n",
      "arithimetic mean =  0.0333295630725059\n",
      "10 first = 0.07492276018341892\n",
      "arithimetic -1 = 0.06139954007632198\n",
      "1.8 = 1.48\n",
      "geometric = -0.10545711797115376\n",
      "mode = -0.01522199652509465\n",
      "max_min_2 = 0.04706582251232638\n",
      "only even = 0.021297215261795843\n",
      "\n",
      " Gaussian case\n",
      "real mean = 0\n",
      "arithimetic mean =  0.053396902510757474\n",
      "10 first = 0.089910519746742\n",
      "arithimetic -1 = 0.056207265800797344\n",
      "1.8 = 1.98\n",
      "geometric = nan\n",
      "mode = 0.2793368083400198\n",
      "max_min_2 = 0.018272844130105537\n",
      "only even = 0.06310179331507319\n",
      "\n",
      " Gaussian erf case\n",
      "real mean = 4\n",
      "arithimetic mean =  0.41791602080699697\n",
      "10 first = 0.8805882065530612\n",
      "arithimetic -1 = 0.6504379166389453\n",
      "1.8 = 2.02\n",
      "geometric = 0.2622929561720557\n",
      "mode = 0.8354412967833884\n",
      "max_min_2 = 0.4995568799706067\n",
      "only even = 0.37572900051771185\n"
     ]
    }
   ],
   "source": [
    "#bias\n",
    "print('Bias test for the estimators for size 20 sample with 10 realizations. \\n ')\n",
    "\n",
    "#uniform sample\n",
    "arithimetic_mean_list = []\n",
    "ten_first_list = []\n",
    "arithimetic_1_list = []\n",
    "one_eight_list = []\n",
    "geometric_list = []\n",
    "mode_list = []\n",
    "max_min_2_list = []\n",
    "only_even_list = []\n",
    "\n",
    "for trow in range(0,100):\n",
    "\n",
    "    uniform_sample = [np.random.uniform(0,1) for i in range(0,20)]\n",
    "    uniform_estimators = tarefa1.mean_estimators(uniform_sample)\n",
    "    \n",
    "    arithimetic_mean_list.append(uniform_estimators.arithimetic())\n",
    "    ten_first_list.append(uniform_estimators.ten_first())\n",
    "    arithimetic_1_list.append(uniform_estimators.arithimetic_1())\n",
    "    one_eight_list.append(uniform_estimators.one_eight())\n",
    "    geometric_list.append(uniform_estimators.geometric())\n",
    "    mode_list.append(uniform_estimators.mode())\n",
    "    max_min_2_list.append(uniform_estimators.max_min_mean())\n",
    "    only_even_list.append(uniform_estimators.only_even())\n",
    "\n",
    "    \n",
    "    \n",
    "print('Uniform case')\n",
    "print('real mean = ' + str(0.5))\n",
    "print('arithimetic mean =  ' + str(abs(np.sum(arithimetic_mean_list)/100-0.5)))\n",
    "print('10 first = ' + str(abs(np.sum(ten_first_list)/100-0.5)))\n",
    "print('arithimetic -1 = ' + str(abs(np.sum(arithimetic_1_list)/100-0.5)))\n",
    "print('1.8 = ' + str(abs(np.sum(one_eight_list)/100-0.5)))\n",
    "print('geometric = ' + str(abs(np.sum(geometric_list)/100)-0.5))\n",
    "print('mode = ' + str(abs(np.sum(mode_list)/100)-0.5))\n",
    "print('max_min_2 = ' + str(abs(np.sum(max_min_2_list)/100-0.5)))\n",
    "print('only even = '+ str(abs(np.sum(only_even_list)/100-0.5)))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#gaussian sample\n",
    "arithimetic_mean_list = []\n",
    "ten_first_list = []\n",
    "arithimetic_1_list = []\n",
    "one_eight_list = []\n",
    "geometric_list = []\n",
    "mode_list = []\n",
    "max_min_2_list = []\n",
    "only_even_list = []\n",
    "\n",
    "for trow in range(0,100):\n",
    "\n",
    "    sampler_gaussiano = tarefa1.sampler(pairs_gauss)\n",
    "    gaussian_sample = sampler_gaussiano.sample(20)\n",
    "    gaussian_estimators = tarefa1.mean_estimators(gaussian_sample)\n",
    "    \n",
    "    arithimetic_mean_list.append(gaussian_estimators.arithimetic())\n",
    "    ten_first_list.append(gaussian_estimators.ten_first())\n",
    "    arithimetic_1_list.append(gaussian_estimators.arithimetic_1())\n",
    "    one_eight_list.append(gaussian_estimators.one_eight())\n",
    "    geometric_list.append(gaussian_estimators.geometric())\n",
    "    mode_list.append(gaussian_estimators.mode())\n",
    "    max_min_2_list.append(gaussian_estimators.max_min_mean())\n",
    "    only_even_list.append(gaussian_estimators.only_even())\n",
    "\n",
    "    \n",
    "    \n",
    "print('\\n Gaussian case')\n",
    "print('real mean = ' + str(0))\n",
    "print('arithimetic mean =  ' + str(abs(np.sum(arithimetic_mean_list)/100-0)))\n",
    "print('10 first = ' + str(abs(np.sum(ten_first_list)/100-0)))\n",
    "print('arithimetic -1 = ' + str(abs(np.sum(arithimetic_1_list)/100-0)))\n",
    "print('1.8 = ' + str(abs(np.sum(one_eight_list)/100-0)))\n",
    "print('geometric = ' + str(abs(np.sum(geometric_list)/100)-0))\n",
    "print('mode = ' + str(abs(np.sum(mode_list)/100)-0))\n",
    "print('max_min_2 = ' + str(abs(np.sum(max_min_2_list)/100-0)))\n",
    "print('only even = '+ str(abs(np.sum(only_even_list)/100-0)))\n",
    "\n",
    "\n",
    "#gaussian_erf sample\n",
    "arithimetic_mean_list = []\n",
    "ten_first_list = []\n",
    "arithimetic_1_list = []\n",
    "one_eight_list = []\n",
    "geometric_list = []\n",
    "mode_list = []\n",
    "max_min_2_list = []\n",
    "only_even_list = []\n",
    "\n",
    "for trow in range(0,100):\n",
    "\n",
    "    sampler_gausserf = tarefa1.sampler(pairs_gausserf)\n",
    "    gaussianerf_sample = sampler_gausserf.sample(20)\n",
    "    gaussianerf_estimators = tarefa1.mean_estimators(gaussianerf_sample)\n",
    "    \n",
    "    arithimetic_mean_list.append(gaussianerf_estimators.arithimetic())\n",
    "    ten_first_list.append(gaussianerf_estimators.ten_first())\n",
    "    arithimetic_1_list.append(gaussianerf_estimators.arithimetic_1())\n",
    "    one_eight_list.append(gaussianerf_estimators.one_eight())\n",
    "    geometric_list.append(gaussianerf_estimators.geometric())\n",
    "    mode_list.append(gaussianerf_estimators.mode())\n",
    "    max_min_2_list.append(gaussianerf_estimators.max_min_mean())\n",
    "    only_even_list.append(gaussianerf_estimators.only_even())\n",
    "\n",
    "    \n",
    "    \n",
    "print('\\n Gaussian erf case')\n",
    "print('real mean = ' + str(4))\n",
    "print('arithimetic mean =  ' + str(abs(np.sum(arithimetic_mean_list)/100-4)))\n",
    "print('10 first = ' + str(abs(np.sum(ten_first_list)/100-4)))\n",
    "print('arithimetic -1 = ' + str(abs(np.sum(arithimetic_1_list)/100-4)))\n",
    "print('1.8 = ' + str(abs(np.sum(one_eight_list)/100-4)))\n",
    "print('geometric = ' + str(abs(np.sum(geometric_list)/100)-4))\n",
    "print('mode = ' + str(abs(np.sum(mode_list)/100)-4))\n",
    "print('max_min_2 = ' + str(abs(np.sum(max_min_2_list)/100-4)))\n",
    "print('only even = '+ str(abs(np.sum(only_even_list)/100-4)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c0b86d14",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Efficiency test for the estimators for size 20 sample with 10 realizations. \n",
      " \n",
      "Uniform case\n",
      "real mean = 0.5\n",
      "arithimetic mean =  0.0034135626265573114\n",
      "10 first = 0.007602183328305296\n",
      "arithimetic -1 = 0.003782340860451315\n",
      "1.8 = 0.0\n",
      "geometric = 0.005973298886728999\n",
      "mode = 0.08917916085095019\n",
      "max_min_2 = 0.0006878657466063894\n",
      "only even = 0.005351352429663604\n",
      "\n",
      " Gaussian case\n",
      "real mean = 0\n",
      "arithimetic mean =  0.06288326151368526\n",
      "10 first = 0.07148463413401476\n",
      "arithimetic -1 = 0.06967674405948504\n",
      "1.8 = 0.0\n",
      "geometric = nan\n",
      "mode = 0.5263188122094642\n",
      "max_min_2 = 0.1495823894758904\n",
      "only even = 0.06582146027853522\n",
      "\n",
      " Gaussian erf case\n",
      "real mean = 4\n",
      "arithimetic mean =  0.05836985517643245\n",
      "10 first = 0.1403760693310272\n",
      "arithimetic -1 = 0.0646757398076814\n",
      "1.8 = 0.0\n",
      "geometric = 0.049676768036638806\n",
      "mode = 0.6903287839715523\n",
      "max_min_2 = 0.08063059922194389\n",
      "only even = 0.0835864529447496\n"
     ]
    }
   ],
   "source": [
    "#efficiency\n",
    "print('Efficiency test for the estimators for size 20 sample with 10 realizations. \\n ')\n",
    "\n",
    "#uniform sample\n",
    "arithimetic_mean_list = []\n",
    "ten_first_list = []\n",
    "arithimetic_1_list = []\n",
    "one_eight_list = []\n",
    "geometric_list = []\n",
    "mode_list = []\n",
    "max_min_2_list = []\n",
    "only_even_list = []\n",
    "\n",
    "for trow in range(0,10):\n",
    "\n",
    "    uniform_sample = [np.random.uniform(0,1) for i in range(0,20)]\n",
    "    uniform_estimators = tarefa1.mean_estimators(uniform_sample)\n",
    "    \n",
    "    arithimetic_mean_list.append(uniform_estimators.arithimetic())\n",
    "    ten_first_list.append(uniform_estimators.ten_first())\n",
    "    arithimetic_1_list.append(uniform_estimators.arithimetic_1())\n",
    "    one_eight_list.append(uniform_estimators.one_eight())\n",
    "    geometric_list.append(uniform_estimators.geometric())\n",
    "    mode_list.append(uniform_estimators.mode())\n",
    "    max_min_2_list.append(uniform_estimators.max_min_mean())\n",
    "    only_even_list.append(uniform_estimators.only_even())\n",
    "\n",
    "    \n",
    "    \n",
    "print('Uniform case')\n",
    "print('real mean = ' + str(0.5))\n",
    "print('arithimetic mean =  ' + str(np.sum((arithimetic_mean_list-np.sum(arithimetic_mean_list)/10)**2)/10))\n",
    "print('10 first = ' + str(np.sum((ten_first_list-np.sum(ten_first_list)/10)**2)/10))\n",
    "print('arithimetic -1 = ' + str(np.sum((arithimetic_1_list-np.sum(arithimetic_1_list)/10)**2)/10))\n",
    "print('1.8 = ' + str(np.sum((one_eight_list-np.sum(one_eight_list)/10)**2)/10))\n",
    "print('geometric = ' + str(np.sum((geometric_list-np.sum(geometric_list)/10)**2)/10))\n",
    "print('mode = ' + str(np.sum((mode_list-np.sum(mode_list)/10)**2)/10))\n",
    "print('max_min_2 = ' + str(np.sum((max_min_2_list-np.sum(max_min_2_list)/10)**2)/10))\n",
    "print('only even = '+ str(np.sum((only_even_list-np.sum(only_even_list)/10)**2)/10))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#gaussian sample\n",
    "arithimetic_mean_list = []\n",
    "ten_first_list = []\n",
    "arithimetic_1_list = []\n",
    "one_eight_list = []\n",
    "geometric_list = []\n",
    "mode_list = []\n",
    "max_min_2_list = []\n",
    "only_even_list = []\n",
    "\n",
    "for trow in range(0,10):\n",
    "\n",
    "    sampler_gaussiano = tarefa1.sampler(pairs_gauss)\n",
    "    gaussian_sample = sampler_gaussiano.sample(20)\n",
    "    gaussian_estimators = tarefa1.mean_estimators(gaussian_sample)\n",
    "    \n",
    "    arithimetic_mean_list.append(gaussian_estimators.arithimetic())\n",
    "    ten_first_list.append(gaussian_estimators.ten_first())\n",
    "    arithimetic_1_list.append(gaussian_estimators.arithimetic_1())\n",
    "    one_eight_list.append(gaussian_estimators.one_eight())\n",
    "    geometric_list.append(gaussian_estimators.geometric())\n",
    "    mode_list.append(gaussian_estimators.mode())\n",
    "    max_min_2_list.append(gaussian_estimators.max_min_mean())\n",
    "    only_even_list.append(gaussian_estimators.only_even())\n",
    "\n",
    "    \n",
    "    \n",
    "print('\\n Gaussian case')\n",
    "print('real mean = ' + str(0))\n",
    "print('arithimetic mean =  ' + str(np.sum((arithimetic_mean_list-np.sum(arithimetic_mean_list)/10)**2)/10))\n",
    "print('10 first = ' + str(np.sum((ten_first_list-np.sum(ten_first_list)/10)**2)/10))\n",
    "print('arithimetic -1 = ' + str(np.sum((arithimetic_1_list-np.sum(arithimetic_1_list)/10)**2)/10))\n",
    "print('1.8 = ' + str(np.sum((one_eight_list-np.sum(one_eight_list)/10)**2)/10))\n",
    "print('geometric = ' + str(np.sum((geometric_list-np.sum(geometric_list)/10)**2)/10))\n",
    "print('mode = ' + str(np.sum((mode_list-np.sum(mode_list)/10)**2)/10))\n",
    "print('max_min_2 = ' + str(np.sum((max_min_2_list-np.sum(max_min_2_list)/10)**2)/10))\n",
    "print('only even = '+ str(np.sum((only_even_list-np.sum(only_even_list)/10)**2)/10))\n",
    "\n",
    "\n",
    "#gaussian_erf sample\n",
    "arithimetic_mean_list = []\n",
    "ten_first_list = []\n",
    "arithimetic_1_list = []\n",
    "one_eight_list = []\n",
    "geometric_list = []\n",
    "mode_list = []\n",
    "max_min_2_list = []\n",
    "only_even_list = []\n",
    "\n",
    "for trow in range(0,10):\n",
    "\n",
    "    sampler_gausserf = tarefa1.sampler(pairs_gausserf)\n",
    "    gaussianerf_sample = sampler_gausserf.sample(20)\n",
    "    gaussianerf_estimators = tarefa1.mean_estimators(gaussianerf_sample)\n",
    "    \n",
    "    arithimetic_mean_list.append(gaussianerf_estimators.arithimetic())\n",
    "    ten_first_list.append(gaussianerf_estimators.ten_first())\n",
    "    arithimetic_1_list.append(gaussianerf_estimators.arithimetic_1())\n",
    "    one_eight_list.append(gaussianerf_estimators.one_eight())\n",
    "    geometric_list.append(gaussianerf_estimators.geometric())\n",
    "    mode_list.append(gaussianerf_estimators.mode())\n",
    "    max_min_2_list.append(gaussianerf_estimators.max_min_mean())\n",
    "    only_even_list.append(gaussianerf_estimators.only_even())\n",
    "\n",
    "    \n",
    "    \n",
    "print('\\n Gaussian erf case')\n",
    "print('real mean = ' + str(4))\n",
    "print('arithimetic mean =  ' + str(np.sum((arithimetic_mean_list-np.sum(arithimetic_mean_list)/10)**2)/10))\n",
    "print('10 first = ' + str(np.sum((ten_first_list-np.sum(ten_first_list)/10)**2)/10))\n",
    "print('arithimetic -1 = ' + str(np.sum((arithimetic_1_list-np.sum(arithimetic_1_list)/10)**2)/10))\n",
    "print('1.8 = ' + str(np.sum((one_eight_list-np.sum(one_eight_list)/10)**2)/10))\n",
    "print('geometric = ' + str(np.sum((geometric_list-np.sum(geometric_list)/10)**2)/10))\n",
    "print('mode = ' + str(np.sum((mode_list-np.sum(mode_list)/10)**2)/10))\n",
    "print('max_min_2 = ' + str(np.sum((max_min_2_list-np.sum(max_min_2_list)/10)**2)/10))\n",
    "print('only even = '+ str(np.sum((only_even_list-np.sum(only_even_list)/10)**2)/10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6091578b",
   "metadata": {},
   "source": [
    "Questão 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "d8fad705",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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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xK681HrNrc5rMsSJuMksV3r4a6jeFg0a4TpM6+Q2h3/WwZJY394sxGWJF3GTWd5Pg+ynQ5ypouK3rNKm118mww57w7o0Q3ug6jckRdnk2kzmxGLx3IzTbmU6vtaLstZpNZuVyEqzKbDFssfgWeGowfDIK2MVdKJMzrCVuMmfBa7B0DvS9ljLyXKdJj/YHQcfDYOpdNGGt6zQmB1gRN5kRDcOkW6BlZ9jzBNdp0qv/9bBpNcWhuvUfg8lOVsRNZsx+GlZ+B/3/DwJ1c5rZlNlhT9jjWM4Ovs12rHadxmQ5K+Im/crWw+Tboc1+0GmA6zSZ0fca6lPGBaGxrpOYLGdF3KTfzEdg7c/Q/28gPj+xJ1EtOvJKtDenB99lB1a4TmOymI1OMVuVyIRRW12mbJ03OVT7vlDYMy0ZayqRUS61mWCrtRzH4OB0hoVeo3DEdr8/XuuJt4wpx1riJr1mPgbrf8muE3sStFgLeD7aj5OCk2kjy1zHMVnKirhJn7L18OG93rC7nfd3ncaJ+yNHEyXAsODrrqOYLGVF3KRPyeOwrhT65F4rfLPlNOf5aF+ODX7ATtgFxE3qWRE36VG2HqbfA+36QNsertM4NSpyFAqcH3rDdRSThayIm/SY9YTXCs/BvvCKlrIdL0X7cGJwMtuz0nUck2VsdIpJvfAGmD4S2h0IbQ8A3M53ko5tJ7vOB6ODODE4OX4W5+kpz2Nyl7XETerNGgNrl+V0X3hFi7Ulr0Z7cUrwPVhrfeMmdayIm9SKlMGH90HbXnVuXLhrD0YHk08YPrrPdRSTRRIu4iISFJHZIvJmOgMZn5v7IqxZAr0vc52kzvleW/FmrAd88iist75xkxrJtMQvAb5IVxDjf0IMpt0DO3SFDv1dx6mT7o8cDeF1MOMh11FMlkioiItIa+BI4NH0xjF+dmigBFZ8A70uy505UpL0jbaG3QfBx6Ng4xrXcUwWSLQlfg9wJVDlFWBFpFhESkSkpLTUDtzkHvVm7Nu2PXQe7DpM3dbrMti02jsAbEwtVTvEUEQGAstVdZaIHFTVcqo6GhgNUFRUpKkKaOqmikPsDgjMZ+/AQug5MvvnC6+tnbp5wy9nPAj7/RlC9VwnMj6WSEu8JzBIRBYBzwP9ROTptKYyvnNBcCzLtBnsNcR1FH/oeSn8thQ+f9F1EuNz1RZxVb1aVVuraiFwMjBJVU9LezLjG3vKQnoH5/Fo5AhrVSaqQz/vAPD0kd4FpI2pIRsnbmrtgtBYVmtDnov2cx3FP0Sg5yXegeCvxrtOY3wsqSKuqpNVdWC6whj/6SBLGBCYyVPRQ1lLQ9dx/KXz0dCsLUz7F6gdRjI1Yy1xUyvFwXFsIo8nIjly7cxUCobggL/AkhL4YbrrNManbAIsU2M7sIJjgh/wbLQ/K2kCJHY5N1POPqd5F5Gedg8U9rKfn0matcRNjZ0beosAyiMRKzY1ltcA9jsfvp0IP89zncb4kBVxUyNNWMuQ4CTGxg5gCQWu4/jbn86FvEbeSBVjkmRF3NTIacH32EY2Wis8FRpuC93Pgnkv01rsbGeTHCviJnmRTZwVeoep0T35Qtu6TpMdelwIIpwbtOGGJjlWxE3yPn+BlrKKUVEbbZoyTVvDnidycvB9mmMTY5nE2egUk7DCEeMQYkzMv41NtGV6rIvrSL5U1aXdOsreTKz3LKcH3+Xe6LFVvsZGrZjyrCVuktIvMJtdAj8xKnIUYNPNptI32pp3o/twZugd6rPJdRzjE1bETVKKQ+NYrC0YF9vPdZSsNCpyFNvJb5wQnOI6ivEJK+ImYfvIN+wX+JLHIocTxaabTYeZuiuzYh05LzgOohHXcYwPWBE3CSsOvckqbcQL0b6uo2QxYVRkIDsHSuGL112HMT5gRdwkpFCWclighKejB7Oe+q7jZLWJse58F2vlnfxjE2OZalgRNwkZGhxPmCBPRg5zHSXrKQFGRwfC0jmceu0/qhzNYgxYETcJ2I7VHB+cysvR3pTSzHWcnPBqtBfLtRl/Dr7pOoqp46yIm2qdEZpAPhEejdr45EwpI4/HIwM4MDiXPWSR6zimDrMibraqARs5IziRd2PdWKg7uo6TU56N9uc3bUBxyFrjpmpWxM1WnRCcQnNZy6iInWKfaWtoxLPRfgwMfERrWe46jqmjrIibqkUjDA2OZ1asI7N0V9dpctLjkcOJEmCoTYxlqmBF3FTti7HsHChltLXCnVnGtrwW7cVJwck2MZaplE2AZf7AG9KmjM2/iUa0YmKsey3WY2prdPRITgxN4YzgREZGj3Mdx9Qx1bbERaS+iHwiInNEZL6I3JiJYMatHoEFdA18z6PRI4jZP2xOfautmRjtZhNjmUol8uncBPRT1b2AvYEBIrJ/WlMZ54qDb1KqTXgl2tt1FAM8HDmKbWUtJwYnu45i6phqi7h61sbv5sVvdi5wFuskP9I3OIcnI4exiXzXcQwwS3elJNaJ84LjbWIss4WE/k8WkaCIfAYsByaq6seVLFMsIiUiUlJaatcJ9LPi0DjWaz2ejh7sOoopZ1RkIG0CpbDgNddRTB2SUBFX1aiq7g20BvYVkT9c0kVVR6tqkaoWFRTY1c99a81PDApM54XoQayises0ppx3Y934NrajTYxltpDU6BRVXSUi7wMDgHnpiWQypbLRI9eEnuGcoPJY9HAHiczWKAFGRQdy58+jYeH70KFf0uuwy7xln0RGpxSISLP49w2AQ4Av05zLONCUtZwafJc3Yj1YrC1dxzGVeD3aE7bZwWuNG0Ni3SmtgPdF5HNgJl6fuE3mkIXODE6gkWziocgg11FMFcrIg/0vgIWT4afPXMcxdUAio1M+V9V9VLWrqnZR1ZsyEcxkVgM2clbobSZGu/G1tnEdx2xN0dlQrwl8eK/rJKYOsLM4DABDgu+zray1Vrgf1G/qFfL5r8Kvi1ynMY5ZETfkEWFoaBwzYrvzqXZyHcckYr8LQILw4f2ukxjHbO4Uw9HBaewoKxkRPs91FJOoJq1gr5PY8MmT9PygOytpssXTNvIkd1hLPMcFiHF+8A3mxQqZGuvqOo5JxgGX0EDKOCM0wXUS45AV8Rx3aKCEDoGl8b5wcR3HJKOgExOi3TkjOIEGbHSdxjhiRTynKReGXmdhbAfeiu3rOoypgf9NjDXFdRTjiBXxHNYrMI+uge8ZFT3Kppv1qU+1E5/EdqU49CZ52MRYucg+uTnswuDr/KzNeTXay3UUUwv3RY5hJ1nBccGprqMYB2x0Sq764SMOCC7g5vBp3lmAxrc+iO3J7NguXBR8nZeiBxJJ08fa5l2pm6wlnqum3E6pNuWZaH/XSUytCSMjx9AmUMoxwWmuw5gMsyKei/77MSyczKjIQDZSz3UakwKTY3vzeawdFwVfJ0jUdRyTQVbEc9GUf0DDFtYKzyrCvZFjKQwsY1DgQ9dhTAZZEc81i0vgu/fggL+wgfqu05gUejfWjQWxtgwLvQYxa43nCiviuWby7dBwO/jTUNdJTMoJ90aOoUNgqTc5lskJVsRzyZJZ8O1E6DEM6m3jOo1Jg3diRXwVaw1T7oBYzHUckwFWxLNU4Yhxv99+N+UOaNAc9rWJrrKVEuC+yDHwy1fwxeuu45gMsCKeK36aDV+/DT0ugnp2AeRsNj62H7TY1es6s77xrGdFPFdMuiXeCv+z6yQmzWIEoO/VUPolzH3JdRyTZlbEc8Gi6fDtu9DrcqjfpPrljf/tPhh26AqTb4Vo2HUak0ZWxLOewqSboXEr6wvPJYEA9Lveu3zb7H+7TmPSyIp4ljso8Bn89yM48ArIa+A6jsmkjodAm/29A9rhDa7TmDSpdqYcEWkDPAVsDygwWlVHpjuYqT0hxhWhF6F5IXQ7A9hyEiPjTwm/hyLQ/3oYcyTMfAwOGJbeYMaJRFriEWC4qnYG9gcuEpHO6Y1lUuGIwCfsEfgB+l4LQZupMCcV9oIO/WDa3bDpN9dpTBpUW8RVdamqfhr//jfgC2CndAcztRMkyuWh//BlrA10Oc51HONSv+tg/Qr46EHXSUwaJNUnLiKFwD7Ax5U8VywiJSJSUlpamqJ4pqaOD06lQ2Apd0VOgEDQdRzj0k7dYbeB8OG9tGC16zQmxRIu4iKyDfAycKmqrqn4vKqOVtUiVS0qKChIZUaTrE1rGR76D7NiHZkY6+46jakLDr4RIhu5JPSy6yQmxRIq4iKSh1fAn1HVV9IbydTah/fSUlZxS/g07Ar2BoAWu0DROQwJTqKDLHGdxqRQIqNTBHgM+EJV705/JFMra36C6ffyRnR/ZmtHwEakmLg+V7H+439zdehZhoavcJ3GpEgiLfGewOlAPxH5LH47Is25TE1NugU0yj8iJ7tOYuqaRi14IHI0Bwdn0yMw33UakyKJjE6Zpqqiql1Vde/4bXwmwpkkLZ0Dnz0L+53PYm3pOo2pg8ZED2OxtuDa0DM2VW2WsDM2s4UqvHOtN8lV7+Gu05g6ahP53BE+iS6BRfD5C67jmBSwIp4tvhoPiz6Ag66GBs1cpzF12BuxHnwW6wDv3gAb/zDQzPiMFfFsEN4Ab4+Agt2g6GzXaUwdpwT4W/hMWLsMpt7hOo6pJSvi2WDav2DVf+GIf9rp9SYhc3QX6HY6zHgIln/pOo6pBSvifrdyIUy7B7ocD+16u05jfKTbhwewOprPtPvO8Y6pGF+yIu53b43wWt+H3uI6ifGZlTThzshJ9ArOhwWvuY5jasiKuJ999RZ88w70uQqatHKdxvjQs9H+zI+19UY2bVrrOo6pASviflW2Dt660juYuf8FrtMYn4oR4Prw2bBmCbx/q+s4pgasiPvVpL97BzOPvNsOZppa+VQ7QdG58PFDsHiW6zgmSVbE/WjxLO8DV3QOFPZ0ncZkg4NvgG12gLF/gUiZ6zQmCdVOgGXSo/ykVItuPzLhx/OI8Eb+tTSVZhwy7QDmDcxAWOM7Vf0eVal+EzjyLnh+CEwfCX1sgiy/sJa4z5wfHMtugR+5Lnw2a2noOo7JJrsdAXsc450AVPq16zQmQVbEfaST/Miw0Gu8Ed2f9+xiDyYdDr8D8hrC2GEQi7pOYxJgRdwn8glzT96D/EZDbgif6TqOyVbbtPQK+Y8fe90qps6zIu4Tl4ZepnPgB0aEz2MFTV3HMdms64nQ+WhvyOHSOa7TmGpYEfeDHz7i/OAbPBfpy7vWjWLSTQQG/gsabgevFEN4o+tEZitsdEpdt3ENvFrMj1rALZHTtrqoXYbNVCbZ34vNyx8YOJOn8v8B790IA25LRzSTAtYSr8tUYdxwWL2Yy8MXsI4GrhOZHDI1thfsWwwzHoSvJ7iOY6pgRbwumzUG5r4IB13NLN3VdRqTiw65CbbfE14tphUrXKcxlbAiXkftIYvgraugQ3/o/VfXcUyuymsAJ4yBaIQH8keSR8R1IlOBFfE6qDHreSBvpHdg6djRELC3yTjUYhcYdC/dAt9yZeh512lMBdVWBxF5XESWi8i8TATKdUKMO/NG0VpK4YQnoFEL15GMgS7HMiZyKOeFxjMg8InrNKacREanjAHuB55Kb5TsV9UogfKPXxp6hQHBmdwcPo3rd96/xus0JtVujZzKXoGF3J33ECw9Dlp1/cMySc/ZYmqt2pa4qk4FVmYgS847MjCDS0Ov8J/IgTwWPdx1HGO2UEYexWWXs4pG8NwQ+G2Z60iGFPaJi0ixiJSISElpaWmqVpszushC/pn3MCWxTlwbORcQ15GM+YNSmnFe2XBYvwJeONVOBKoDUlbEVXW0qhapalFBQUGqVpsTdqKUR/PvYiWNOb/sMsqwizyYumu+toNjHobFM+MTZcVcR8ppNuzBseas4an822nIJs4pu4JfbF4U4wd7HA39roe5/4EJ13onphkn7LR7hxqwkcfz/0lr+YXTy0bwle7sOpIxies9HNaVemd0NiqA3pe7TpSTqi3iIvIccBDQQkQWA39T1cfSHSzb5RPmwbyRdJXvuCB8KZ/o7q4jGZMcETjsNlj3ize/SsPtABsSm2mJjE4ZoqqtVDVPVVtbAa+9fMI8lHcPfYNzuCYylAmxP7mOZEzNBAJ0LBnElGhXomMv4ZjAB64T5RzrE8+wfMI8kDeS/sHZXBM+lxeifV1HMqZWwoQ4P3wpM2KduSvvYY4LTHUdKadYEc+gepTxQN5IDgl+ynXhs3k22t91JGNSYgP1OTf8V6bH9uDOvFGcEJzsOlLOsCKeKRtW8VT+7fQPzOa68Nk8HT3EdSJjUmoj9Rga/ivTYl24M280fHi/60g5wYp4Jvz2M4w5kn3kGy4OD7MCbrLWJvI5LzycN6P7eUMP377GxpGnmRXxdPt5Hjx6CKz8nnPCV/JmrIfrRMak1Sby+Uv4L7Df+TDjAXj5XAhvcB0ra+X0OPG0T9azYCy8ej7UbwJnj2PavT8l9XKb3Mr4lRKgcEpvioOruWb+c7ByIZz8DDRtvcVyNmFW7VlLPB1iUXj/NnjxdNi+MxRPhh33cZ3KmAwTRkePYmjZcFjxHYzqA4umuw6VdayIp9qapfDUYJhyO+x1Cpz5JjTewXUqY5x5N9YdzpsEDZrBU4Ng6j+9ho5JCSviqfT1BHi4JyyZBYMfgKMfhLz6rlMZ415BJ6+Q7z4IJt0MTx4Fq350nSorWBFPhQ2/wmsXwrMnQONWXvfJPqd5pyUbYzz1m8Lxj8PRD8PSOfBwz/iJQTZ5Vm1YEa+tBWPhgf1gzvPQ63IY+h4U2JXpjamUCOw9BM7/AAp24678h3km71YKZanrZL4lmoYpJIuKirSkpCTl662pqo6A1+bI+CFXj+K60NP0CX4OO3SFwfdDq73+MKKkqu0Zk6t+/0zEYlx7/XCuCj1PPcI8GBnE6OiRbKD+lsuRns9wXSMis1S1KNnXWUs8Wet+gXHDeSt/BHsHvuXm8GleX1+rvVwnM8ZfAgGeiR5M/013MjHWncvyXmZyvcs5Kfg+QezAZ6Jyepx4UtYuhw/vhZmPQWQTT0cPZmTkWH6lCdcH7Uo8xtRUKc0ZFr6YxyMDuCbvWf6R9whDg+NhzgbochwErUxtjbXEq7NyIbw1Au7pCh89ALsfBRd9zA2Rs/iVJq7TGZM1PtVOHF/2N/5cdilRAvBqMdzXDWY+Sj3KXMers+xPXGViMfhuEnwyCr6ZCIEg7HkC9P4rtNglvtDXTiMak52Ed2L7MqGsiO/PCsIHd8G44cyotw0vR3vbzJ+VsCJe3rIF8PkLMPclWLMYGrWEPldB97OgSSvX6YzJGUoAdjsCdj0cFk1j+uM3c2ZwAkNDb8GY171G1e5HuY5ZJ+R0ERdidJFF9AvMhoduhWXzQIKwS3845EbvxIRQvuuYxuQuEWjXm2HhSyhgFScEp3Dl6k/gjYth3OU8kbcH42L7Mzm6t+ukztS5IYaJDBlKdljRFstfvTf89yNYOJnln75BS1lFTIVPtSNjoz0YF92fFeWuOJ9IBmNMJild5HsGBmcwMDiD1vILAPNihUyNdWVqrCuzY7uwiT82wNIxDDFVwxxrOsQwu1viZeth+QJODb5Lt8DX7Ctfwb9KvefqNeWT2O68F92HKbG9WGkHKY3xCWGetmdepD23R4awhyyiT+Bz+gTncF5wHBeGxhLWIPO1LZ/GOvFprCOfa3t+1ALXwdMiO4r4hl+9USQrFnpff/kKfp4LK74FjfH3PCjVJsyM7UabAcNh5x6wfReGXfuO6+TGmFoR5ms75kfb8WB0MNuwnv0CX9A98A3dA18zJDiJc0JvA7BO68Eje3ozi7bcA7brAM3bQbOdfd1tmlARF5EBwEggCDyqqrenNVUCWvIro/Pvhn9c5BXx8pruDK26emNMd9iTnmNKWUILQFi0v7/P6jLGVG0tDXkv1p33Yt0BCBFhd/kvnQM/sJv8l7Pz1sMXb8KnT/3vRRLw5jnf5RAYeLej5DVXbREXkSDwAHAIsBiYKSJjVXVBusNtzWoasU7rQ+ejYdv23l/VbdtD80LIa7DFskuw/mtjclGEEHO1PXOj7QE4+6wjQdU7eW/lQvj1e1j5vfe1QXPHaWsmkZb4vsC3qroQQESeBwYDTov4JvI5NXwti46ylrUxJgki0Hh779bW/5dLrHZ0iogcDwxQ1aHx+6cD+6nqsArLFQPF8bu7Al/VMFML4JcavjYb2P7n7v7n8r6D7f+uqto42Rel7MCmqo4GRtd2PSJSUpNhNtnC9j939z+X9x1s/0WkRuOyE5k7ZQnQptz91vHHjDHGOJZIEZ8JdBSRdiKSD5wMjE1vLGOMMYmotjtFVSMiMgx4B2+I4eOqOj+NmWrdJeNztv+5K5f3HWz/a7T/aTnt3hhjTGbYfOLGGONjVsSNMcbHnBVxERkgIl+JyLciMqKS588Xkbki8pmITBORzi5ypkt1+19uueNEREUka4ZeJfDenyUipfH3/jMRGeoiZ7ok8t6LyIkiskBE5ovIs5nOmE4JvP//Kvfefy0iqxzETIsE9n1nEXlfRGaLyOcickS1K1XVjN/wDpB+B7QH8oE5QOcKyzQp9/0g4G0XWV3tf3y5xsBUYAZQ5Dp3Bt/7s4D7XWd1uP8dgdlA8/j9lq5zZ3L/Kyz/F7zBFM6zZ+i9Hw1cEP++M7CouvW6aon/fiq/qpYBm0/l/52qril3txGQTUdgq93/uJuBfwAbMxkuzRLd92yVyP6fBzygqr8CqOryDGdMp2Tf/yHAcxlJln6J7LvC7/NiNwV+qm6lror4TsCP5e4vjj+2BRG5SES+A+4ALs5Qtkyodv9FpBvQRlWzbfauhN574Lj4v5MviUibSp73q0T2vxPQSUSmi8iM+Cyi2SLR9x8RaQu0AyZlIFcmJLLvNwCnichiYDzefyJbVacPbKrqA6raAbgKuM51nkwRkQBwNzDcdRZH3gAKVbUrMBF40nGeTAvhdakchNcSfUREmrkM5MjJwEuqGnUdJIOGAGNUtTVwBPDveD2okqsinuyp/M8DR6czUIZVt/+NgS7AZBFZBOwPjM2Sg5vVvvequkJVN8XvPgp0z1C2TEjkd38xMFZVw6r6PfA1XlHPBsl89k8me7pSILF9Pxd4EUBVPwLq400MVjVHHfwhYCHev0qbO/j3qLBMx3LfHwWUuD4wkcn9r7D8ZLLnwGYi732rct8fA8xwnTvD+z8AeDL+fQu8f8G3c509U/sfX243YBHxExKz4Zbge/8WcFb8+93x+sS3+jNwcnk2reJUfhG5Ca9YjwWGicjBQBj4FTjTRdZ0SHD/s1KC+36xiAwCIsBKvNEqWSHB/X8HOFREFgBR4ApVXeEudeok8bt/MvC8xqtZNkhw34fjdZ9dhneQ86zqfgZ22r0xxvhYnT6waYwxZuusiBtjjI9ZETfGGB+zIm6MMT5mRdwYY3zMirgxxviYFXFjjPGx/wfhwAkwcmXfzgAAAABJRU5ErkJggg==\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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mSaCGiOwbR18f+DkuCY0pzC/fwNyn4fg+0KSz12nK5Es9ipeDnbnC/zEnyHdexzEprMQCr6q3q2p9Vc0CLgSmq+olwKfAee5ifYD34pbSmPxCQZh4I1TNhM5DvE4TkaHBi/iF2jySNgry9ngdx6SoaMbB3wYMEJFVOPvk/xebSMaU4MuRsGExnDEUKtfwOk1EnF01V3GYbz189rjXcUyKKlOBV9UZqnqWe32NqrZW1caqer6q7o1PRGPy2fajs++9SRdo2tPrNFGZEz6GCaFTnGGeW1Z7HcekIPsmq0keqvDBIOd6t8ec86MmuQfzLoFAJfhwkNM+Y2LIJhszCetvk22tmAwrJ8M/7ocah3iYLHZyqAGn3Qkf3wbLJmL/kiaWrAdvkkMwFybfDrWbQOurvU4TW62uhAOPgY9vp4rNHW9iyAq8SQ5fjoRf10DXhyGQYtMe+QPQbRjs+JnrAu96ncakECvwJuHVYTvMfMQ5sNrkdK/jxEeD1tC8F1f6P+Jg7BvfJjaswJuEd0tgLAR/hy4Peh0lvjrdgwK3po31OolJEVbgTUI7WtZwvn8mnHQN1GnsdZz4ql6fUaFu9PB/znGy0us0JgVYgTcJTLk9MIatVIP2t3gdplyMDJ7NJq3BXWmvYedxNdGyAm8SVnvfYk7xZ/NU8ByoVN3rOOViN5V4LHg+J/hW0s33pddxTJKzAm8SkhBmcOBNfgxn8kaok9dxytW40KksCx/CbYExpBEs+QnGFMEKvElIZ/s+p6nvBx4L9iKXNK/jlKswPoYGL+QQXw4X+qd7HcckMSvwJuGkk8egwNssCWfxfvgkr+N4Ykb4WL4MH8mNgQkRnxjEGCvwJuH09k+lgS+Hh4MXoRX2T1R4JK8XmbKdK/yTvQ5jkpRNfGFi4m/zxkRoP3ZzfWACn4WOZnb4mFhEi7t4nTpvgR7B1NBxXB14H/Zshco147Idk7oqavfIJKgr/B9TS3YyNHih11ESwmPBXuzHHmdKYWPKyAq8SRy/76Bv4EOmhE5giR7qdZqEsFwPYWL4ZPhiJPy2wes4JslYgTeJY97zVJfd/Dd4jtdJEsqw4PkQzoNZj3odxSQZK/AmMezdCXNH8GnoWL613vtf/Kh14fjLYMHLsG2d13FMErECbxLD/NGwe4vzrVXzd+0GOj9nD/M2h0kqVuCN93J3w+dPwaEd+FoP9zpNYqpe3+nFf/0q9djsdRqTJGyYpPHEX4ZV9vwRdm2C9i/B0m0lLx/FMMyk1m4AfP0K/QPvcVewr9dpTBKwHrzxVAa5zhDAhm0h6xSv4yQ2txd/gX+G9eJNqViBN5463z8TflsPp1aM6YCj1m4AAP0D73kcxCQDK/DGM2kEuTYwERqcCI1O9TpOcqhen7Gh07jAP8NO7WdKZAXeeOZc/ywOli3Q/lYQ8TpO0ngm2AOA/oGJHicxic4KvPFEgCD9/e+xMHwoNK5Y871Haz21GRs6jfP9M2Dbj17HMQnMCrzxRE//HA7x5Tjj3q33XqKswR/8cYE/e/F89riHqUyiK7HAi0glEflKRBaJSLaI3Ofe30hEvhSRVSIyVkTS4x/XpISQ03vPDjdkWvh4r9MkpX29eL55Hbb/5HUck6BK04PfC3RU1WOBFkBXETkJGAo8oaqNga2ADcw1pZP9Dof6NrhzzljvPVIjg90Bdb4kZkwhSizw6tjp3kxzLwp0BMa5978M9IxHQJNiwiGY9RjLww34JNzS6zRJ7WcyofmFsOAl2LnJ6zgmAZVqH7yI+EVkIbAJmAKsBrap6r4zAv8EHFzEc/uJyHwRmZ+TY8O6Kryl78Hm73gqeE4FPltTDLW9GUK5MHeE10lMAirVf5iqhlS1BVAfaA0cWdoNqOooVW2pqi0zMzMjS2lSQzgMsx6DOofzUbi112lSQ53G0OwcmPcC7P7V6zQmwZRpLhpV3SYinwInAzVEJOD24usDP8cjoEk+RZ3CrotvHs+lZ/Pv3P6Eo+i927w0BbQbCEvGw1ejoMNgr9OYBFKaUTSZIlLDvV4Z6AwsAz4FznMX6wPYd6dNMZQbAhP4PlyXSeGTvQ6TWuo2gyO6wRfPwu87vE5jEkhpulEHAZ+KyGJgHjBFVScBtwEDRGQVUBv4X/ximmTX0fcNR/vWMiLUkxB+r+OknvYD4fdtMN/+Dc2fStxFo6qLgeMKuX8Nzv54Y0qg3BiYwLpwJu+GbMbIuDj4BDisk3OwtfXVkF7F60QmAdgwBhN37X2LaeFbzYhQD4J2CoL4aT8IduXA1694ncQkCCvwJs6c3vvPWpvxofZeh0ltDdtAw1Pg8/9CcK/XaUwCsO6UiauTfUtp6VvBXXlXkBeHP7eiRuwk2jrLQ9bgD2jra89r6XNg0Rg44XKvIxmPWQ/exNWN/gls1Bq8HbL53svD7PDRzgyds5+AULDkJ5iUZgXexE0rWc7J/qWMDHZnLzYXXfkQng6eA1vXOmPjTYVmBd7EzQ2BCeTo/owJdfQ6SoUyLXwcHNDMmUo4HPY6jvGQFXgTF8fJStr7v2VU8Cx+J8PrOBWK4nPGxW/+Dpa/73Uc4yEr8CYubghM4Fetxuuh072OUjE17Qm1Gztz/6h6ncZ4xAq8ibljZA0d/Qt5IdiN3VTyOk7F5PND2wGwYTGs/MTrNMYjVuBNzN0QmMA2rcoroc5eR6nYml8ANQ7hm9fuIGvwpKQd/mkiZwXexNRR8gP/8C9gdPAMdmJfl/eUPw3a3sxxvlW09S3xOo3xgBV4E1PXByawQyvzUqiL11EMQItL+EVrcUNggtdJjAeswJuYaSI/0c3/FS+FurCDql7HMQCBDEYGu3OibzknyjKv05hyZgXexMz1gXfZqZUYHTzD6ygmn7Gh09ikNbgh8I7XUUw5swJvYuJQ+YXuvrm8GurMNvbzOo7JZy/pPBfsRlt/Nvz4pddxTDmyycZMTFwXeI+9pPFC8MwyP9dGd0SuqN9dwfvfCHWif2AitWc9Ar1tCoOKwnrwJnq/rqGHbw6vhU5nC9W9TmMKsYdKvBDsBqumws8LvI5jyokVeBO9WY8TxM+ooJ0AO5G9EuoMlWo43241FYIVeBOdX7+HRWN4I9SJHGp6ncYUYxeV4aT+8N2HsOFbr+OYcmAF3kTns8fBF2BksLvXSUxpnHg1ZOwPsx71OokpB1bgTeS2rv3jzEGbrPeeHCrXcIr80omwycbFpzobRVOB5R9psfbhsu0/zxr8AQ8Fnueffmg/65hYRzPxdFJ/+OJZ3ntqAP/Oux4o++tvkoP14E1E6ksO5/lnMSbUkY3U8jqOKYsqtaBVX87yzaWRrPc6jYkjK/AmIv397xFGbN97sjr5BnJJ47rAe14nMXFkBd6U3bZ1nOefydjQaWygttdpTCSqZfJGqBM9fbNpIBu9TmPixAq8KbvZwwB4Nni2x0FMNJ4LnkUQPzf6babJVGUF3pTNtnXw9au8FerAeuu9J7VN1OS10On80/8ZbF7ldRwTByWOohGRBsArQF1AgVGq+qSI1ALGAlnAWuACVd0av6imvBQ7umb2EwA8E+xRnpFMjBSco+bZ4Nlc7J9OlZkPw7kvRLQeG4GTuErTgw8CA1W1KXAScJ2INAUGA9NUtQkwzb1tUtm2H+GbV+G43vxCHa/TmBjYQnXn5CzfjoONS72OY2KsxAKvqutV9Wv3+m/AMuBgoAfwsrvYy0DPOGU0iWLmUECg/SCvk5gYGhXsBunVYMZDXkcxMVamffAikgUcB3wJ1FXVfYNoN+DswinsOf1EZL6IzM/JyYkmq/HS5lWwcAy06gvV63udxsTQNvaDk6+DZRNh/SKv45gYKnWBF5FqwHjgJlXdkf8xVVWc/fN/o6qjVLWlqrbMzMyMKqzx0IwHIVAJ2g7wOomJh5P7OzNNfvqg10lMDJWqwItIGk5xf11V9533a6OIHOQ+fhCwKT4Rjec2fAtLxsNJ10A1e5NOSZWqQ5sbYMXH8NN8r9OYGCmxwIuIAP8DlqnqsHwPTQT6uNf7APaVuFQ1/QHIcAuASV0nXgNVasOnD3idxMRIaSYbOwW4FPhWRBa6990BPAy8JSJ9gR+AC+KS0Hhr3TxY8RF0vBsq24yR8ZAwpyzMqAZtb4ZP7oK1cyDrFBsOmeRKLPCqOhuQIh7uFNs4JuFM/w9UzXR6dyb1tewLc0fA1Huh7ydepzFRsm+ymiKd7MuG72c6B1Yzqnkdx5SH9CrQ4Xb46StYPsnrNCZKVuBNoYQwgwNjYP/60PJfXscx5anFJVDnCJh6H35CXqcxUbACbwrV3fcFx/rWQMe7IK2S13FMefIH4PR7YctKevlneBzGRMMKvPmbdPK4JTCW7HBDaN7L6zjGC0ecAYeczE2B8VTmd6/TmAjZKfvM31zm/4QGvhwuyb2d131/9gESZrSHiT8R6DyEA/7XmSv9H/JU6J9eJzIRsB68+avdv3JDYAIzQscyJ2znWq3QGrTmo1Arrg5MojbbvU5jImAF3vzVZ4+zH3t4OHiR10lMAng02ItK5HJDwE4KkoyswJs/bV0LX41iXKg9y/UQr9OYBLBG6/Fm6DQu8U+DnBVexzFlZAXe/GnqfSB+Hg+e73USk0CGBc9nDxkw+Q6vo5gysgJvHD98DtnvQJsb2Egtr9OYBPIr+/Nk8J+wagqssG+3JhMbRZOiyjKHiI8wfHir86WmtjfDJ5/GO55JYIWNlnol9A/uPvBLmHw7HNqh/EOZiFgP3nCRfzps/Ba63O98Vd2YAvIIQNeHYMsq+GqU13FMKVmBr+Cqs5NBgbcgqx007el1HJPImnSGJv+AmUOpY8Mmk4IV+ApuQOBt9mcXnDHU+XKLMcXp8iDk7WZQYKzXSUwpWIGvwI6UH+ntn8qroc5Qt5nXcUwyqNMETryGCwMzOF5s2GSiswJfUYXDDEl7ke1U5YngeV6nMcmkw2DWay0eSBtts00mOCvwFdU3r9Da9x0PBS9mOzbXuymDjP24N+8yjvL9yOX+j71OY4phwyQrot82wpR7+CJ8FG+HTgVsIjFTNpPDrZgaOo4BgXGw/Q6oXr9Mz7dTAZYP68FXRJPvgLw93JHXl6LPxmhMcYR7g5fjQ+Gj27wOY4pgBb6iWTkVloyDdgNZo/W8TmOS2E+a6XzDdfkk+O4jr+OYQliBr0hyd8MHA6B2E+cbq8ZE6YXQmXBAU5h0M+zZ5nUcU4AV+Ipk+v2w7QfoPhwCGV6nMSkgSAB6jICdm2DynV7HMQVYga8ofvgcvngGWl0JWW29TmNSycHHQ9ubYOFrsHKK12lMPjaKpgJoOng8H6UPBjJpePp9XscxCSjqUVSn3gbLP2T9a/3osncoO6j6l9ExNkrLG9aDrwAGB8bQQHIYlHcNZNiYdxMHgQzo+QyZbOPOwOtepzEuK/Apro1vCZcFpjA61JV5eqTXcUwqO/h4Roa60yswg06+BV6nMViBT2nV2cljaSNZHT6IR4O9vI5jKoD/Bv9Jdrghj6SNgt82eB2nwiuxwIvIaBHZJCJL8t1XS0SmiMhK92fN+MY0Zac8kjaKOmzn33nXsZd0rwOZCiCXNG7Mu54q7IUJ10A47HWkCq00PfiXgK4F7hsMTFPVJsA097ZJIL39U+nin8/Q4EUs0UO9jmMqkNV6MPcFL4M1n8Lcp72OU6GVOIpGVWeJSFaBu3sAHdzrLwMzAPu+cgzEZI6ODUu4O/Aa00Mt+F/ojBglMxVdWUbCvBk6jYebb4RpQ6BRuzimMsWJdB98XVVd717fANSNUR4TrdxdMO5fbKcqt+Rdjc01Y7wh0P2/UO0AePty9men14EqpKgPsqqqAlrU4yLST0Tmi8j8nJycaDdniqMK710PW1ZyU15/tlDd60SmIqtSC85/Cbb/zBNpzyLY/vjyFmmB3ygiBwG4PzcVtaCqjlLVlqraMjMzM8LNmVKZ+zRkvwMd7+bz8NFepzEGGrSGrg/Ryf8N1/vf9TpNhRNpgZ8I9HGv9wHei00cE7E1M2HKPXDU2TaRmEksra5kfKgtNwfG08G30Os0FUpphkmOAeYCR4jITyLSF3gY6CwiK4HT3dvGK9vWwbgroM7h0PMZO3m2SSwi3JnXl++0AcPTRtBI1pf8HBMTpRlFc1ERD3WKcRYTid93wJgLIZQHvV6HjP1iunqbQ8TEwu9k0C/vZt5Nv4fRaY9wTu4QtuH8rZZm5JidASoy9k3WZBbKg7cvh03LnINZdRp7nciYIq3TulyVO5B68ivPpT9BOnleR0p5VuCTlSp8OAhWT4OznoDG9oHKJL6v9XAG5V3Nib7lPJz2PMUMwDMxYNMFJ6vZw2DBS9B2AJzQp8TFjUkU74fb0DBvI4PS3uYXrc1jNk9S3FiBT0ZfPe98Q/Do86Dj3V6nMabMng71pJ5s5vrAe+zQKowKdfc6UkqyAp9sFo11ds0cfgacMxJ8tpfNJCPhrmBf9pM93JE2hp1U4Y2Q7WaMNSvwyWTZ+/DutdCovXNQ1Z/mdSJjIhbGx815/anCXu4PjGaXZgA2QiaWrMAni+wJMP5K5/yXF46BtEpA2YeP2bBHE2vR/E0FCdA/79+8lPYIw9KehYXNoUVRI7NNWdnn+2SwaCyM+xfUbwW937HT7pmUspd0/pU3iLnhpvDuNTB/tNeRUoYV+EQ3/0WYcDVktYXe46HS/l4nMibm9lCJvnm3QJMuMOlmmDvC60gpwQp8wlKY/gBMugmadIaL34L0ql6HMiZu9pIOvV5z5lOafAdMvtPOCBUlK/AJKI0gj6c9C7MegeN6w4VvQFplr2MZE3+BdGcAQaurnNlRx10OeXu8TpW07CBrgqnFDp5O+y9t/EvhtLug/SCbPMxULD4/nPko1GwIn9wFO9aTSR9ysFM/l5UV+CgUNXog/2iWoka5FHr/zwt4P+NO6rCDm3Ov5YlTbylxPcYkqkhG1/z17/wGqN4A3r2WSRl30j/33yzQI4pZ3v4vCrJdNIlAFRa8DKO7ogjn5v4fE8J2HktjaNYTrpzKHs3gzfT76eOf7Py/mFKxAu+x6ux0ZoR8/0ZoeArd997PEj3U61jGJI66zTg7935mhI/lvrSX4c2LYaed/rM0rMB76BTft0zOuA2WT4JO/we9x7MVGwZpTEE7qEq/vAEMybsUVk2DZ0+G7z7yOlbCswLvhd2/8lDgeV5Pf4idWhmunAbtBjgHl4wxhVJ8jA6dAf1mQLUDYcyFPJY2klrs8DpawrICX55UnW+lPt2K8/0zeS7YjbNyH4B6LbxOZkzyqNsUrpoG7QbSwzeH6RkD6eX/1MbMF8JG0ZSTFrIKXuoGP8yBg1vSfetAlmlDoOyjDYpa3uaZMRVGIAM63cOZU+tyf9pohqY9D6MXQuf/QMOT/7JoNPM1lWZEXCKzHnycZcl6RqQN592Me2DzSjhrOPSd8kdxN8ZEbqXWp1fu3QzMvcY5+fyLXWHMRc5pLI0V+LjZuBTGX8XU9Fvo4FvEE3nnwo3fQMsrbA53Y2JKGB9u7/x/dboH1s6GZ9s4o9N+Weh1OE/ZLpqYUk7yLYMxr8F3H0JaVUaHzuD5YDdyqMHNNgukMfGTXgXaDYQTroA5w2HeaMiewCtpx/Bc6CzmhI/2OmG5swIfA/uzk/P8n3GJfyqH+dbDjzWhw+3Quh8PDpnrdTxjKpYqtaDzEOd8xfNHc9TU4bzuf4jvw3Vhzmo49mKolul1ynJhBT5Subs50/cF3f1z6ehbSIbk8XW4MQNyr2HYnffa5GDGeK1yDWg3gLYfNOJM35dcFJhOoyn3wLT/wOFdoNk5cHjXlD6/ghX4stiZA6unw8rJ8N3HPJO+i01agzdCHXk7dCpLNQuAYVbcjUkYe0lnQrgdE3LbsXbAYfD1K7BkvPMFw0AlZzruI8+CwzpCtQO8jhtTSVPgYzXUqTTL7Lu/Knto4VtFa99yOvgWcYx8j08UqtSB5udz0dyD+TJ8FOECx6ptGKMx0Svr/1Gp/ueHrQZOQTiZ76+t7ZwKc+l7zvmOgexwQ24LNGd2+GgWhhvHLL9XwyqTpsDHXTAXNq+AjUu4LzCOlr4VHCk/4hclpMI32oRhwfMY1L8/HNQCfD7mzrGCbUwyUnzQsI1z6TqUbnc+w6m+xbT3L+ZK/4dcG3ifkAo8+4RzqswGrTlStrNa65GXRGUzeZLGgirs2Qpbv4eta+nv/5jDfT9xpKyDBy+DcBCA8/wZfBNuzNPhc5gfPpyF4cb8RhUABh18vJctMMbEms9HtjYiO9SIZ0I9qMoejvet5ATfCm6qts3ZnbPgRT7OgDz1s0YPgnHj4YCjoNZhUDPLuVSumXDnboiqwItIV+BJwA+8oKoPxyRVrM0dAYvHwq9rYe/2P+6+NQ1+1tosDx/CkW3Oh7rNoO7RNB+2ghA2L4wxFdEuKvNZuDmfhZtz06XdnCkQNq/gxuGvcrhvHUfIOo74aZ5T+PPLqO6cpKRZT2e4ZgKIuMCLiB8YAXQGfgLmichEVV0aq3AxVTXT+ahVs5HzblurEU2fWM5uKgGw9vQ/95GFWO1RSGNMwvH54IAjmRhuA+50N2tv6ga5u2Dr2r9fEmi++mh68K2BVaq6BkBE3gR6AIlX4E++zrkUsJu15Z/FGJMa0qu6n/qbeZ2kSKIRvtuIyHlAV1W90r19KXCiql5fYLl+QD/35hHAdxFmrQNsjvC5icralPhSrT1gbUoGBdvTUFXL/O2suB9kVdVRwKho1yMi81W1ZQwiJQxrU+JLtfaAtSkZxKo90cx69TPQIN/t+u59xhhjEkA0BX4e0EREGolIOnAhMDE2sYwxxkQr4l00qhoUkeuByTjDJEeranbMkv1d1Lt5EpC1KfGlWnvA2pQMYtKeiA+yGmOMSWx25gljjElRVuCNMSZFJUSBF5GuIvKdiKwSkcHFLHeuiKiItHRvXyIiC/NdwiLSotyCFyOKNqWJyMsi8q2ILBOR28svddGiaE+6iLzotmeRiHQor8wlKalNInK5iOTk+/u6Mt9jfURkpXvpU77JixZlmz4WkW0iMql8Uxct0vaISAsRmSsi2SKyWER6lX/6wkXRpoYi8rV7X7aIXFPixlTV0wvOAdrVwKFAOrAIaFrIcvsBs4AvgJaFPH4MsNrr9kTbJuBi4E33ehVgLZCVxO25DnjRvX4AsADwJcNrBFwOPF3Ic2sBa9yfNd3rNZO5Te5jnYDuwCSv2xKD1+hwoIl7vR6wHqiR5G1KBzLc69Xc2lCvuO0lQg/+jykPVDUX2DflQUH/AYYCvxexnovc5yaCaNqkQFURCQCVgVxgR5zzliSa9jQFpgOo6iZgG5AIX0gpbZsK0wWYoqq/qupWYArQNU45yyKaNqGq04Df4hUuAhG3R1VXqOpK9/ovwCYgEc7TF02bclV1r3szg1LsgUmEAn8wsC7f7Z/c+/4gIscDDVS1uAnYewFjYh8vItG0aRywC6fH8SPwmKr+GsespRFNexYBZ4tIQEQaASfw1y/IeaXENrnOdT/ijxORfblL+9zyFk2bElFM2iMirXF6v4kwi2BUbRKRBiKy2F3HUPfNq0iJUOCLJSI+YBhQ5PybInIisFtVl5RbsCiU0KbWQAjnY2UjYKCIHFqO8cqshPaMxvkjng8MBz7HaV8yeB9n91hznF76yx7niYVUa1Ox7RGRg4BXgStUNexBvkgU2SZVXefe3xjoIyJ1i1tRIhT4kqY82A84GpghImuBk4CJ+w7iuS4kcXrvEF2bLgY+VtU8d5fGHLzfpRFxe1Q1qKo3q2oLVe0B1ABWlE/sYpU41Yaqbsn3kfgFnE8fpXquR6JpUyKKqj0isj/wAXCnqn4R56ylFZPXyO25LwHaFbu1BDjoEMA5SNWIPw86NCtm+RnkO8iK8yb1M3Co122JRZuA2/jzoGRVnOmXmydxe6oAVd3rnYFZXr8+pW0TcFC+6+cAX7jXawHf4xxgreler5XMbcp3XwcS5yBrNK9ROjANuMnrdsSwTfWByu71mjgdpWOK3Z7XDXbDnumGXY3zbgswBDi7kGULFvgOBf9IE+ESaZtwjo6/DWS7xf0Wr9sSZXuycKaIXgZMxZn21PP2lKZNwEPu67AI+BQ4Mt9z/wWsci9XeN2WGLXpMyAH2IOzW61LsrYH6A3kAQvzXVp43Z4o29QZWOzevxjoV9K2bKoCY4xJUYmwD94YY0wcWIE3xpgUZQXeGGNSlBV4Y4xJUVbgjTEmRVmBN8aYFGUF3hhjUtT/A87ggx35hwKhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#letra a\n",
    "\n",
    "L_list = [2,8,16,64,1024]\n",
    "for L in L_list:\n",
    "    z_inter_list =  np.random.uniform(0,1,1000)\n",
    "    for i in range(0,L):\n",
    "        z_new_list = np.random.uniform(0,1,1000)\n",
    "        z_inter_list = z_inter_list + z_new_list\n",
    "    \n",
    "    z_list = []\n",
    "    for i in range(len(z_inter_list)):\n",
    "        z_list.append(z_inter_list[i]/L)\n",
    "        \n",
    "    \n",
    "    z_mean = np.sum(z_list)/len(z_list)\n",
    "    z_var = np.sum((z_list - z_mean)**2)/len(z_list)\n",
    "    \n",
    "    \n",
    "    x_list = np.linspace(z_mean - 3*np.sqrt(z_var),z_mean + 3*np.sqrt(z_var),1000)\n",
    "    plt.hist(z_list,density = True,bins = 100)\n",
    "    plt.plot(x_list,stats.norm.pdf(x_list,z_mean,np.sqrt(z_var)))\n",
    "    plt.title('Uniform distribution with L = ' + str(L))\n",
    "    plt.show()\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9b4b721e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5082205506103611\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.12433168708905\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.06257305865172522\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01567063532884563\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": [
    "#letra b\n",
    "\n",
    "L_list = [2,8,16,64]\n",
    "for L in L_list:\n",
    "    sampler_gaussiano = tarefa1.sampler(pairs_gauss)\n",
    "    gaussian_sample = sampler_gaussiano.sample(1000)\n",
    "    z_inter_list =  gaussian_sample\n",
    "    for i in range(0,L):\n",
    "        z_new_list = sampler_gaussiano.sample(1000)\n",
    "        z_inter_list = z_inter_list + z_new_list\n",
    "    \n",
    "    z_list = []\n",
    "    for i in range(len(z_inter_list)):\n",
    "        z_list.append(z_inter_list[i]/L)\n",
    "        \n",
    "    \n",
    "    z_mean = np.sum(z_list)/len(z_list)\n",
    "    z_var = np.sum((z_list - z_mean)**2)/len(z_list)\n",
    "    \n",
    "    \n",
    "    x_list = np.linspace(z_mean - 3*np.sqrt(z_var),z_mean + 3*np.sqrt(z_var),1000)\n",
    "    plt.hist(z_list,density = True,bins = 100)\n",
    "    plt.plot(x_list,stats.norm.pdf(x_list,z_mean,np.sqrt(z_var)))\n",
    "    plt.title('Gaussian distribution with L = ' + str(L))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ab998e1d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\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": [
    "#letra c\n",
    "\n",
    "L_list = [2,8,16,64,1024]\n",
    "for L in L_list:\n",
    "    gaussian_sample_1 = np.random.normal(0,1,1000)\n",
    "    gaussian_sample_2 = np.random.normal(2,2,1000)\n",
    "    z_inter_list =  gaussian_sample_1+gaussian_sample_2\n",
    "    for i in range(0,L):\n",
    "        z_new_list = np.random.normal(0,1,1000) + np.random.normal(2,2,1000)\n",
    "        z_inter_list = z_inter_list + z_new_list\n",
    "    \n",
    "    z_list = []\n",
    "    for i in range(len(z_inter_list)):\n",
    "        z_list.append(z_inter_list[i]/(2*L))\n",
    "        \n",
    "    \n",
    "    z_mean = np.sum(z_list)/len(z_list)\n",
    "    z_var = np.sum((z_list - z_mean)**2)/len(z_list)\n",
    "    \n",
    "    x_list = np.linspace(z_mean - 3*np.sqrt(z_var),z_mean + 3*np.sqrt(z_var),1000)\n",
    "    plt.hist(z_list,density = True,bins = 100)\n",
    "    plt.plot(x_list,stats.norm.pdf(x_list,z_mean,np.sqrt(z_var)))\n",
    "    plt.title('Gaussian distribution with L = ' + str(L))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8e3762d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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