NeganSmith92/ISSUES6.ipynb

## ISSUES6.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "52fcce79",
   "metadata": {},
   "outputs": [],
   "source": [
    "#EXERCISE_1\n",
    "# 1.Explain the difference between median and middle value?\n",
    "# 2.Are mean and mode values always the same for unsorted and sorted dataset? Why?\n",
    "# 3.If range is caculate with last datapoint – first datapoint, should the dataset is sorted first or not? Why?\n",
    "\n",
    "\n",
    "# 1.The median is a measure of central tendency that represents the middle value of a dataset when it is ordered from smallest to largest. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values.\n",
    "#   The middle value is simply the value that occupies the middle position in a dataset. It does not necessarily have to be the median. For example, in the dataset [1, 3, 5, 7, 9], the median is 5, while the middle value is also 5 because it occupies the middle position. However, in the dataset [1, 2, 3, 4, 5, 6], the median is (3 + 4) / 2 = 3.5, but the middle value is 4.\n",
    "\n",
    "# 2.The mean (average) and mode (most frequent value) may or may not be the same for unsorted and sorted datasets.\n",
    "#   For the mean, sorting the dataset does not change the sum of the values, so the mean remains the same whether the dataset is sorted or not.\n",
    "#   For the mode, sorting the dataset may change the frequency distribution of the values, potentially affecting which value appears most frequently and thus changing the mode. However, if there is a single mode (one value that appears most frequently), it will remain the same regardless of sorting.\n",
    "\n",
    "# 3.It doesn't matter whether the dataset is sorted or not when calculating the range. The range is simply the difference between the maximum and minimum values in the dataset.\n",
    "#   Sorting the dataset does not change the maximum and minimum values, so whether the dataset is sorted or not, the range will be the same.\n",
    "#   Therefore, sorting the dataset is unnecessary and does not affect the calculation of the range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "de193fbe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[34, 66, 41, 68, 32, 72, 78, 37, 49, 58, 41, 33, 34, 47, 41, 10, 68, 77, 38, 20, 34, 61, 49, 64, 48, 56, 11, 62, 46, 67, 43, 28, 68, 37, 66, 13, 50, 41, 74, 43, 40, 77, 72, 11, 79, 78, 33, 38, 53, 11, 45, 23, 50, 66, 58, 44, 47, 65, 12, 63, 41, 40, 70, 36, 45, 27, 14, 77, 42, 17, 54, 64, 24, 23, 56, 15, 51, 32, 36, 31, 28, 54, 10, 72, 61, 31, 57, 21, 59, 72, 46, 42, 38, 73, 16, 13, 24, 13, 80, 43]\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_2\n",
    "import random as rnd\n",
    "x = [\n",
    "    rnd.randint(10, 80)\n",
    "    for i in range(0, 100)\n",
    "]\n",
    "print(x)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(x, bins=25, color='red', edgecolor='black')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Histogram of Random Data by zafran marvis')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# In this example, I've chosen bins=25 to divide the data into 25 equally spaced bins.\n",
    "# Because to make the histogram look didn't worst and the detailed information is easy to read.\n",
    "# You can adjust the number of bins based on your preference and the distribution of your data.\n",
    "# If you have more data points or if you want more detailed information about the distribution, you may consider increasing the number of bins.\n",
    "# Conversely, if you have fewer data points or if you want a broader overview of the distribution, you may consider decreasing the number of bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4ac1eb33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_3\n",
    "import numpy as np\n",
    "import statistics as stat\n",
    "N = 1000; a = 20; b = 60; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)\n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(20, 64, 4))\n",
    "plt.xlim([20, 60])\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# n = b - a + 1 = 60 - 20 + 1 = 41\n",
    "# Average Value = N * 1/n * the width of the bins = 1000 * 1/41 * 4 = 97,5609"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "027f2e30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_4\n",
    "N = 6000; a=1; b=6; dice = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    dice.append(xi)\n",
    "plt.hist(dice, bins=6)\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# if we choose bin = 6, The value is 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f585227f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wAQAQHh5uMj0pKQnTpk0DcHOLoLy8HLNnz0ZJSQkGDBhQ7xaBi4sLJk6ciPLycgwfPhzJycl1tgjmzZunnMU0duxYrFu3riljJCIiIgdkUYjhFgERERHZC947iYiIiFSJIYaIiIhUiSGGiIiIVIkhxkp4NhMREVHrYoghIiIiVWKIISIiIlViiKkHvxoiIrJP7M90K4YYIiIiUiWGGCIiIlIlhhgiIiJSJYYYIiIiUiWGGCIiIlIlhhgiIiJSJYYYIiIiUiWGGCvi9QuIiJqPvZTMxRBDREREqsQQQ0RERKrEEENERESqxBBzG34XS0REpA4MMURERKRKDDFERESkSgwxREREpEoMMURERKRKDDFERESkSgwxREREpEoMMbfg6dVERETqwRBDREREqsQQY2Xcm0NE1LLYZ6kWQwwRERGpEkMMERERqRJDDBEREakSQwwRERGpEkPM/8MDxYiIbI+9mCzBENMCuBISERG1PIYYIiIiUiWGGCIiIlIlhhgiIiJSJYYYIiIiUiWGmBbCg3uJiIhaFkMMERERqRJDDLjXhIhIbdi3CWCIISIiIpViiCEiIiJVYohpQdzdSURkPvZMslSbDzFcaYiIiNSpzYcYIiIiUieGmBbGPT1EREQto02HGAYMIiL1Yg+nNhti+MtPRGQ/2JOpKew+xKxfvx5BQUFwd3dHaGgovv76a1svksW4chKRmjhC36W2wa5DzJYtWxAXF4fFixcjNzcXjz32GEaPHo0zZ840a762CBUMMkSkBi3Vd1sKe2vb5mLrBWjM6tWrMX36dMyYMQMAsGbNGvzzn//Ehg0bkJiYaFJbUVGBiooK5bnRaAQAlJaWmtQFx/+zSctSXXkdtXOqrvgdNVJj8Ty6vPgxCpaObNLnk23U/v6IiI2XhKh1tETfNUdNxe91ppnbd5vyeWS/LOq7YqcqKirE2dlZ0tPTTabPmzdPhgwZUqc+Pj5eAPDBR4s8ioqKWutXn8hm2Hf5sKeHOX3XbvfE/Prrr6iuroa/v7/JdH9/fxQXF9epX7hwIebPn688r6mpweXLl+Hr6wsnJyerLFNpaSkCAwNRVFQEnU5nlXnaEsdzZyKCsrIyBAQEWGV+RPaMfbflcTx3ZknftdsQU+v2FUFE6l05NBoNNBqNybS77rqrRZZJp9M5xC9fLXPHc+TIEXzwwQf46quvcOrUKXh6eqJ3795YtGgRHn/88Tr1P//8MxYsWIA9e/agqqoKYWFheOONN/DII4/UqU1LS8OKFStw4sQJ+Pj4YOLEiXj99dfh5eXVYuMxl16vt9q8iNSAfbeuadOmYe/evTh16pRV5mfOeM6ePYv//d//RW5uLo4dOwaj0YikpCRMmzat3vrdu3djyZIlOHbsGDw9PREVFYWVK1fCz8/PKsvcGFv1Xbs9sLdDhw5wdnauk/4vXrxYZyuBWsdHH32Eb7/9Fs899xw+++wzbNy4ERqNBsOHD8f//d//mdReunQJjz32GH744Qd88MEH+Mc//oHr168jPDwchYWFJrUpKSmYPHky+vXrh507dyI+Ph7JycmYMGFCaw6PqM1j323YkiVLkJGR0aqf+eOPPyIlJQVubm74r//6r0Zrc3JyMHr0aPj7++Ozzz7DW2+9hd27d2P48OEmxy05HKt8kdpC+vfvLy+88ILJtF69esmrr75qk+UxGo0CQIxGo00+39osHc8vv/xSZ1pVVZWEhITIvffeazL9T3/6k7i6usqpU6dMPq9Dhw4yceJEk/d36tRJIiMjTd6fkpIiAGTHjh0tNh4iqot9t2VZMp7q6mrl74cPHxYAkpSUVG9tv3795IEHHpAbN24o0/bv3y8AZP369c1e7obY+udjt3tiAGD+/PnYuHEjPvjgA3z//fd48cUXcebMGcyaNcsmy6PRaBAfH19n92ljEhIS4OTkhOPHj+Opp56CXq+Hj48P5s+fj6qqKhQWFmLUqFHQarXo1q0bVq5cafL+5ORkODk51dmFuXfvXjg5OWHv3r2tNp76dkk6OzsjNDQURUVFJtMzMjLw+OOPo2vXrso0nU6HCRMm4PPPP0dVVRUA4NChQ7hw4QKeffZZk/c/9dRT8PLysmjLpyk/HyIy5Qh911KXLl1CTEwMAgMDodFo0LFjRzz66KPYvXu3UjNt2jR069at2Z9lyXjatTPvv+hz587h8OHDiI6OhovLf44SGTRoEO67774W3YNk675r18fETJo0Cb/99huWLVuGCxcuIDg4GDt27DD5j7E1aTQaJCQkNOm9EydOxDPPPIPnn38eWVlZWLlyJW7cuIHdu3dj9uzZWLBgAVJTU/HKK6+ge/fuVvsqRURQXV1d72vOzs7485//DACoqqoy+eU3V1VVFb7++ms8+OCDyrTy8nL89NNPGD9+fJ36kJAQlJeX4+eff8Z9992HgoICZfqtXF1dcf/99yuvm6M5Px8iusmR+q65oqOjcfToUfzlL3/BfffdhytXruDo0aP47bffLJ5XTU0NamoavgRHbd+11oHPABrso7XT9u/fb7XPup2t+65dhxgAmD17NmbPnm3rxWi2mJgY5Sj+iIgI7Nq1C+vWrUN6erryn314eDi++OILpKSkWC3E5OTkYNiwYWbVnjx50uItjYSEBPz444/49NNPlWklJSUQEfj4+NSpr51W2xxq/2yo1loH0RGR+Ryl75pr//79mDFjBmbOnKlMe/LJJ5s0r2XLlmHp0qV3rOvatavV+tud+mhTwpha2H2IcRRRUVEmz3v16oVjx45h9OjRyjQXFxd0794dp0+fttrnhoaG4vDhw2bVWnoa8caNG/GXv/wFL730Ur0rfGNbGre/1lCtNbdWiIjq079/fyQnJ8PX1xcREREIDQ2Fq6trk+YVExNTp9/XpyW+fmmLfZQhppXcnpDd3Nzg6ekJd3f3OtOtefVJLy8vPPTQQ2bVWvJ1UlJSEp5//nnExMRg1apVJq95e3vDycmp3vR/+fJlAP/59/D19QVwc0vi9rMfLl++XO+WBRGRNW3ZsgWvv/46Nm7ciCVLlsDLywvjx4/HypUrYTAYLJqXwWAw65RmawaLW/vo7Ry9j9r1gb0EJeTcforcr7/+atb7c3Jy4OrqatbD3F2bSUlJmDFjBqZOnYq33367zsro4eGB7t27Iz8/v8578/Pz4eHhgXvuuQcA0Lt3b2X6raqqqnDixAkEBwebtUxERE3VoUMHrFmzBqdOncLp06eRmJiI9PT0Bq/H0phly5aZ1W/vvfdeqy1/bZ9sqOc6ch/lnhg7V3uMyvHjx9GzZ09l+rZt28x6v7W/TkpOTsaMGTPwzDPPYOPGjQ1uTYwfPx5r1qxBUVERAgMDAQBlZWVIT0/H2LFjlb0+AwYMQKdOnZCcnIxJkyYp7//kk09w9epVXiuGiFpVly5dEBsbiy+//LJJB8Ta4uuku+++G/3798fmzZuxYMECODs7A7h59mdhYSHi4uKs9ll2xyYndtuRnJwciYqKkk6dOgkAycjIMHm9pqZG4uPjpVOnTuLu7i5Dhw6VgoICk5rr169LbGys+Pr6iqenpzzxxBPKPR9q7y1y6dIlk/dMnTpV2rdvX2d5hg4dKg8++KDyvKqqSnr27CldunSR1NRU2blzp8TExEhQUJAAkOzsbJP3L1++XPr27SteXl7SsWNHefLJJ+XEiRNWGdOGDRukXbt28sgjj8j+/fvl4MGDJo/r168r77948aJ06tRJevfuLRkZGbJjxw4ZMmSIaLVa+f77700+a9OmTQJAYmJiJDs7W95991256667ZMSIEbJ+/Xrp3bu3aLVa0Wq1MnDgQJNrxzT350NEra+l+64lrly5Ig8//LCsWrVKPv/8c9m7d6+sWrVK3N3dZcqUKUrd1KlTpWvXrvXOoyX77ttvvy0ff/yxvPHGGwJA5syZIx9//LF8/PHHJu/Nzs4WFxcXGT9+vGRlZUlKSooEBgZKcHCwSW82h5r6bpsPMTt27JDFixfL1q1b612ZVqxYIVqtVrZu3Sr5+fkyadIk6dSpk5SWlio1s2bNkrvvvluysrLk6NGjMmzYMOnTp49UVVU1O8SIiPzwww8SGRkpOp1OOnbsKHPnzpXt27fXG2JGjhwpSUlJUlBQIHl5eTJmzBjp0qWLXL16tdlj8vb2bvRmXSdPnjRZlh9//FHGjRsnOp1OPD09Zfjw4XLkyJF6fw6pqakSEhIibm5uYjAYZN68eVJWVibbtm2T7du3S2FhoRQWFsqiRYvE1dVVWWGa+/MhotbX0n3XEtevX5dZs2ZJSEiI6HQ68fDwkJ49e0p8fLxcu3ZNqWssxLRk322s595u165dMnDgQHF3dxcfHx/5wx/+UO9FSu9ETX23zYeYW92+MtXU1IjBYJAVK1Yo065fvy56vV7efvttEbmZ4l1dXSUtLU2pOXfunLRr104yMzNbbdkbcvHiRQEgOTk5IuIYY/L29paNGzc6xFiI2jr2XXWMyV77Lg/sbcTJkydRXFyMyMhIZZpGo8HQoUNx4MABADdvinjjxg2TmoCAAAQHBys1tmQ0GgH852wgNY+puroaaWlpuHbtGsLCwlQ9FiKqnyOs1+y7rTcWhphG1N4ErbHb0hcXF8PNzQ3e3t4N1tiKiGD+/PkYPHiwcnS6GseUn58PLy8vaDQazJo1CxkZGXjggQdUORYiapza12v23dYdC89OMoO5t6W3tKalxcbG4vjx49i3b1+d19Q0pp49eyIvLw9XrlzB1q1bMXXqVOTk5Civq2ksRGQeta7X7LsNa4mxcE9MI2ovctTYbekNBgMqKytRUlLSYI0tzJ07F9u2bUN2djY6d+6sTFfjmNzc3NC9e3f07dsXiYmJ6NOnD9566y1VjoWIGqfm9Zp9t/XHwhDTiKCgIBgMBmRlZSnTKisrkZOTg0GDBgGAcnnqW2suXLiAgoICpaY1iQhiY2ORnp6OPXv2ICgoyOR1NY7pdiKCiooKhxgLEZlS43rNvmvDsVj1MGEVKisrk9zcXMnNzRUAsnr1asnNzZXTp0+LyM1TyfR6vaSnp0t+fr5Mnjy53lPJOnfuLLt375ajR4/K448/brNTeF944QXR6/Wyd+9euXDhgvL4/ffflRo1jWnhwoXy1VdfycmTJ+X48eOyaNEiadeunezatUt1YyGim9h37XtMauq7DntMTE1NDc6fPw+tVtvod3Bff/21ydUVa+80PXnyZLz99tuYNWsWrly5ovzZt29fpKenQ0SUexwtXboUNTU1eOqpp1BeXo6hQ4ciNTUV165da9lB1mPDhg0Abt4R+1br16/H008/DQCqGlNRURGefvppFBcXQ6fTITg4GFu3bsWAAQNQWlra4mMREZSVlSEgIADt2nHHJVFj2HfDTaaz77Z833USEbHKqO3M2bNnlcvdEzVXUVGRyXfcRFQX+y5Zkzl912H3xGi1WgA3/xF0Op2Nl8YOXbsG1N4r6fx5oH172y6PnSotLUVgYKDy+0REDbN632WfapMs6bvNCjGJiYlYtGgR/vjHP2LNmjUAbu4GWrp0Kd59912UlJRgwIAB+Pvf/44HH3xQeV9FRQUWLFiAjz76COXl5Rg+fDjWr19vkrhKSkowb9485UaHY8eOxdq1a3HXXXeZtWy1uzJ1Oh1DTH3+3w3CAAA6HZvDHdj6tE0iNbB632WfatPM6btN/pL/8OHDePfddxESEmIyfeXKlVi9ejXWrVuHw4cPw2AwYMSIESgrK1Nq4uLikJGRgbS0NOzbtw9Xr15FVFQUqqurlZopU6YgLy8PmZmZyMzMRF5eHqKjo5u6uERERORomnI0cFlZmfTo0UOysrJk6NCh8sc//lFErHd/iH/9618CQA4dOqTUHDx4UADUuTNoQ4xGowAQo9HYlCE6vqtXRYCbj1tuUkam+HtEZD6rry/sU22SJb9HTdoTM2fOHIwZMwYREREm0611T4WDBw9Cr9djwIABSs3AgQOh1+sbvO9CRUUFSktLTR5ERETkuCw+JiYtLQ1Hjx7F4cOH67zW2D0VTp8+rdTc6Z4KxcXF8PPzqzN/Pz+/Bu+7kJiYiKVLl1o6HCIiIlIpi/bEFBUV4Y9//CM2b94Md3f3BuuscU+F+uobm8/ChQthNBqVR1FRUaOfR0REROpmUYg5cuQILl68iNDQULi4uMDFxQU5OTn429/+BhcXF2UPTHPvqWAwGPDLL7/U+fxLly41eN8FjUajHBHPM5KIiIgcn0UhZvjw4cjPz0deXp7y6Nu3L55++mnk5eXhnnvusco9FcLCwmA0GvHtt98qNd988w2MRqNd3EOCiIhaXq8lmfX+naiWRcfEaLVaBAcHm0xr3749fH19lelxcXFYvnw5evTogR49emD58uXw9PTElClTAAB6vR7Tp0/HSy+9BF9fX/j4+GDBggXo3bu3cqBwr169MGrUKMycORPvvPMOACAmJgZRUVHo2bNnswdNpnotycT3q/8/Wy8GERGRRax+xd6XX34Z5eXlmD17tnKxu127dplcee/NN9+Ei4sLJk6cqFzsLjk5Gc63XNgoJSUF8+bNU85iGjt2LNatW2ftxSUiIiKVanaI2bt3r8lzJycnJCQkICEhocH3uLu7Y+3atVi7dm2DNT4+Pti8eXNzF48a0GtJJr639UIQERE1A2/LS0RERKrEEENERKrQ7dXttl4EsjMMMURERKRKDDEEgFs4RESkPgwxbRADCxEROQKGGCIiIlIlhhgiIiJSJYYYIiKyO/zam8zBEENERESqxBBDREREqsQQQ0RERKrEEENERESqxBBDCh5IR0REasIQQ0RERKrEENPGcG8LEdk79ikyF0MMERGpBgMO3YohhoiIiFSJIYaIiIhUiSGGiIiIVIkhhoiIiFSJIYaIiIhUiSGGiIiIVIkhhoiIiFSJIYaIiFSF14qhWgwxREREpEoMMURERKRKDDFtiDm7YLmbloiI1IIhhoiI7AY3pMgSDDFERESkSgwxREREpEoMMURERKRKDDFERESkSgwxREREpEoMMUREdiwxMRH9+vWDVquFn58fxo0bh8LCQpMaEUFCQgICAgLg4eGB8PBwfPfddyY1FRUVmDt3Ljp06ID27dtj7NixOHv2rElNSUkJoqOjodfrodfrER0djStXrrT0EImajCGGiMiO5eTkYM6cOTh06BCysrJQVVWFyMhIXLt2TalZuXIlVq9ejXXr1uHw4cMwGAwYMWIEysrKlJq4uDhkZGQgLS0N+/btw9WrVxEVFYXq6mqlZsqUKcjLy0NmZiYyMzORl5eH6OjoVh0vkSVcbL0AZH+6vbodp1aMsfViEBGAzMxMk+dJSUnw8/PDkSNHMGTIEIgI1qxZg8WLF2PChAkAgA8//BD+/v5ITU3F888/D6PRiPfffx+bNm1CREQEAGDz5s0IDAzE7t27MXLkSHz//ffIzMzEoUOHMGDAAADAe++9h7CwMBQWFqJnz56tO3AiM3BPTBvBC0gROQaj0QgA8PHxAQCcPHkSxcXFiIyMVGo0Gg2GDh2KAwcOAACOHDmCGzdumNQEBAQgODhYqTl48CD0er0SYABg4MCB0Ov1Ss3tKioqUFpaavJoLexpBDDEEBGphohg/vz5GDx4MIKDgwEAxcXFAAB/f3+TWn9/f+W14uJiuLm5wdvbu9EaPz+/Op/p5+en1NwuMTFROX5Gr9cjMDCweQMkshBDDBGRSsTGxuL48eP46KOP6rzm5ORk8lxE6ky73e019dU3Np+FCxfCaDQqj6KiInOGQWQ1DDFERCowd+5cbNu2DdnZ2ejcubMy3WAwAECdvSUXL15U9s4YDAZUVlaipKSk0ZpffvmlzudeunSpzl6eWhqNBjqdzuTRHPyKiCzFEENEZMdEBLGxsUhPT8eePXsQFBRk8npQUBAMBgOysrKUaZWVlcjJycGgQYMAAKGhoXB1dTWpuXDhAgoKCpSasLAwGI1GfPvtt0rNN998A6PRqNQQ2RuLQgyvV0BE1LrmzJmDzZs3IzU1FVqtFsXFxSguLkZ5eTmAm18BxcXFYfny5cjIyEBBQQGmTZsGT09PTJkyBQCg1+sxffp0vPTSS/jyyy+Rm5uLZ555Br1791bOVurVqxdGjRqFmTNn4tChQzh06BBmzpyJqKgonplEdsuiEMPrFRARta4NGzbAaDQiPDwcnTp1Uh5btmxRal5++WXExcVh9uzZ6Nu3L86dO4ddu3ZBq9UqNW+++SbGjRuHiRMn4tFHH4Wnpyc+//xzODs7KzUpKSno3bs3IiMjERkZiZCQEGzatKlVx0tkCScRkaa++dKlS/Dz80NOTo5yvYKAgADExcXhlVdeAXBzr4u/vz/eeOMN5XoFHTt2xKZNmzBp0iQAwPnz5xEYGIgdO3Yo1yt44IEHTK5XcOjQIYSFheHEiRP1bhVUVFSgoqJCeV5aWorAwEAYjcZmf0/rCG7/rtmj8jq+f/O/AQC9XvwE5W7uJq/zOjE3lZaWQq/X8/eIyAzNXV/Ypwiw7PeoWcfE2NP1CniqHxERUdvS5BBjb9cr4Kl+REREbUuTbztQe72Cffv21XnNFtcr0Gg00Gg05iw6ERE5AN4ihZq0J8Yer1dAREREbYtFIYbXK2g7eNEpIiKydxZ9nTRnzhykpqbis88+U65XANy8BoGHh4fJ9Qp69OiBHj16YPny5Q1er8DX1xc+Pj5YsGBBg9creOeddwAAMTExvF5BEzGQEJG9Y5+iprAoxGzYsAEAEB4ebjI9KSkJ06ZNA3DzegXl5eWYPXs2SkpKMGDAgHqvV+Di4oKJEyeivLwcw4cPR3Jycp3rFcybN085i2ns2LFYt25dU8ZIREREDsiiEGPOJWWcnJyQkJCAhISEBmvc3d2xdu1arF27tsEaHx8fbN682ZLFIyIiojaE904iIiIiVWKIISIiIlViiCEiIiJVYoghIiIiVWKIISIi1eKp2W0bQwwRERGpEkOMg+NWChEROSqGGGoQAxAREdkzhhgiIrIpbjBRUzHEEBERkSoxxBAREZEqMcQQERGRKjHEEBERkSoxxBAREZEqMcQQERGRKjHEEBGRqvEU7baLIYaIiIhUiSGGGsUtHCIislcMMQ6MAYSIiBwZQwwRERGpEkMMERHZDPcYU3MwxBAREZEqMcQQERGRKjHEEBERkSoxxNAd8TtrIrJ37FNtE0OMg+IKTUREjo4hhoiIbIIbW9RcDDFERESkSgwxREREpEoMMWQW7vYlInvHPtX2MMQQERGRKjHEEBERkSoxxDgg7lIlInvHPkXWwBBDZmPTISIie8IQQ0REDoMbW20LQ4yD4QpMRPaOfYqshSGGiIiIVIkhhoiIHAr39LQdDDFkETYHImoO9hCyJoYYB8LmQER0E/th22D3IWb9+vUICgqCu7s7QkND8fXXX9t6kdo8Ngcix8a+S2ph1yFmy5YtiIuLw+LFi5Gbm4vHHnsMo0ePxpkzZ2y9aHantYMFgwyRY2rJvsu+QdZm1yFm9erVmD59OmbMmIFevXphzZo1CAwMxIYNG2y9aHbFVo2BDYnI8bRU37VFv+j26nb2KQfnYusFaEhlZSWOHDmCV1991WR6ZGQkDhw4UKe+oqICFRUVynOj0QgAKC0tbdkFtZHg+H826/3VlddR+y9TXfE7aqSmSfPp8uLHAICCpSObtTz2qvb3R0RsvCRELc/afZd9iprCkr5rtyHm119/RXV1Nfz9/U2m+/v7o7i4uE59YmIili5dWmd6YGBgiy2j2ulr/7L+D82f15pmz8KulZWVQa/X37mQSMXsse+yT7Vd5vRduw0xtZycnEyei0idaQCwcOFCzJ8/X3leU1ODy5cvw9fXt976pigtLUVgYCCKioqg0+msMk9b4njuTERQVlaGgIAAq8yPSA3Yd1sOx3NnlvRduw0xHTp0gLOzc530f/HixTpbCQCg0Wig0WhMpt11110tsmw6nc4hfvlqmTueoqIizJs3D8eOHcMvv/wCFxcX3HPPPZg+fTpmzZoFFxfTX6eff/4ZCxYswJ49e1BVVYWwsDC88cYbeOSRR+rMOy0tDStWrMCJEyfg4+ODiRMn4vXXX4eXl1eLjcdc3ANDbQX7bsOmTZuGvXv34tSpU1aZnznjSU9Px8cff4zDhw/j3Llz8Pf3x6OPPoqEhAT06NGjTv3u3buxZMkSHDt2DJ6enoiKisLKlSvh5+dnlWVujK36rt0e2Ovm5obQ0FBkZWWZTM/KysKgQYNstFRt27Vr16DT6bBkyRJs27YNaWlpGDx4MObOnYtZs2aZ1F66dAmPPfYYfvjhB3zwwQf4xz/+gevXryM8PByFhYUmtSkpKZg8eTL69euHnTt3Ij4+HsnJyZgwYUJrDo+ozWPfbdiSJUuQkZHRqp/5xhtv4Pfff8fixYuRmZmJ119/Hbm5uXjkkUfw3XffmdTm5ORg9OjR8Pf3x2effYa33noLu3fvxvDhw02OW3I4YsfS0tLE1dVV3n//ffnXv/4lcXFx0r59ezl16pRNlsdoNAoAMRqNNvl8a7PWeCZOnCguLi5y/fp1Zdqf/vQncXV1NflZGY1G6dChg0ycOFGZVlVVJZ06dZLIyEiTeaakpAgA2bFjh9nL4Wg/HyJbYN9tWZaM55dffqkz7dy5c+Lq6irTp083md6vXz954IEH5MaNG8q0/fv3CwBZv3598xe8Abb++dh1iBER+fvf/y5du3YVNzc3eeSRRyQnJ8dmy3L9+nWJj483+c/6TuLj4wWAHDt2TP77v/9bdDqdeHt7y4svvig3btyQEydOyMiRI8XLy0u6du0qb7zxhsn7k5KSBICcPHnSZHp2drYAkOzs7FYdT33mzJkjbm5uJitP9+7dZeTIkXVqY2JixMPDQ6ndt2+fAJCPPvrIpK6yslK8vLxk5syZZi+HtcZD1Napve9a6uLFizJz5kzp3LmzuLm5SYcOHWTQoEGSlZWl1EydOlW6du3a7M+yxniCgoJMNvzOnj0rACQxMbFO7X333ScjRoxo8mfdia37rt0eE1Nr9uzZmD17tq0XA8DN738TEhKa9N6JEyfimWeewfPPP4+srCysXLkSN27cwO7duzF79mwsWLAAqampeOWVV9C9e3erfZUiIqiurq73NWdnZ/z5z38GAFRVVdU5puVO8ywrK8OuXbuQnJyMl156SXl/eXk5fvrpJ4wfP77Oe0NCQlBeXo6ff/4Z9913HwoKCpTpt3J1dcX999+vvG6O5vx8iOg/HKXvmis6OhpHjx7FX/7yF9x33324cuUKjh49it9++83iedXU1KCmpuFTwWv7blMPfP75559x+vRpjBs3TpnWUB+tnbZ///4mfZY5bN137T7EOIqYmBjlKP6IiAjs2rUL69atQ3p6uvKffXh4OL744gukpKRYLcTk5ORg2LBhZtWePHkS3bp1u2PdG2+8gYULFwK4eRbDokWL8Prrryuvl5SUQETg4+NT572102qbQ+2fDdVa6yA6IqKG7N+/HzNmzMDMmTOVaU8++WST5rVs2bJ6Tzu/XdeuXS3ub1VVVZg+fTq8vLzw4osvKtPv1EebEsbUgiGmlURFRZk879WrF44dO4bRo0cr01xcXNC9e3ecPn3aap8bGhqKw4cPm1Vr7mnE06ZNQ0REBC5fvow9e/Zg1apVMBqNWLt2rUldY1sat7/WUK21TtMkImpI//79kZycDF9fX0RERCA0NBSurq5NmldMTEydfl+f28/quhMRwfTp0/H1119j69at9V6Lpy32UYaYVnJ7QnZzc4Onpyfc3d3rTLfmVYa9vLzw0EMPmVVr7tdJBoMBBoMBwM0reXp7e+PVV1/Fc889h4cffhje3t5wcnKqN/1fvnwZwH/+PXx9fQHc3JK4/RTOy5cv17tlQURkTVu2bMHrr7+OjRs3YsmSJfDy8sL48eOxcuVKpdeZy2AwmHVKsyXBQkQwY8YMbN68GR9++GGdvUS39tHbOXoftdtTrOmm2pBz+ylyv/76q1nvz8nJgaurq1mPpn51079/fwDADz/8AADw8PBA9+7dkZ+fX6c2Pz8fHh4euOeeewAAvXv3VqbfqqqqCidOnEBwcHCTlomIyFwdOnTAmjVrcOrUKZw+fRqJiYlIT0/HtGnTLJ7XsmXLzOq39957r1nzqw0wSUlJ2LhxI5555pk6NbV9sqGe68h9tM2HmK+++gpPPPEEAgIC4OTkhE8//dTkdRFBQkICAgIC4OHhgfDw8Drn51dUVGDu3Lno0KED2rdvj7Fjx+Ls2bNWWb7aY1SOHz9uMn3btm311icmJqJfv37QarXw8/PDqlWrlIsl1T6+/fZbzJw5E76+vnBzc8MjjzyCtLQ0k6+TLBlTdnY2AKB79+7KtPHjx2PPnj0oKipSppWVlSE9PR1jx45V9voMGDAAnTp1QnJyssk8P/nkE1y9ehVubm4ICQlRLqQUFhaGnTt3KnW2/vkQkeXsue926dIFsbGxGDFiBI4ePWrWe27tu2vXrsWQIUPu2Hc7dOhwxzE98cQTmDJlCpKSkvDOO+/g2Wefrffz7777bvTv3x+bN282OZHj0KFDKCwstPgYyw0bNqin79rknCg7smPHDlm8eLFs3bpVAEhGRobJ6ytWrBCtVitbt26V/Px8mTRpknTq1ElKS0uVmlmzZsndd98tWVlZcvToURk2bJj06dNHqqqqlFOsL126ZDLfqVOnSvv27essz9ChQ+XBBx9UnldVVUnPnj2lS5cukpqaKjt37pSYmBgJCgqq9xTrkSNHSlJSkhQUFEheXp6MGTNGunTpIlevXm32mPz9/SUmJkZSUlJk79698umnn8qsWbPE2dlZnnrqKZPluHjxonTq1El69+4tGRkZsmPHDhkyZIhotVr5/vvvTWo3bdokACQmJkays7Pl3XfflbvuuktGjBgh27Ztk+3bt0thYaEUFhbKokWLxNXVVQoKCqzy8yGi1tfSfdcSV65ckYcfflhWrVoln3/+uezdu1dWrVol7u7uMmXKFKWusVOsW6rv3n333QJAnn32WTl48KDJ4+jRoybLkJ2dLS4uLjJ+/HjJysqSlJQUCQwMlODgYItPf1ZT323zIeZWt69MNTU1YjAYZMWKFcq069evi16vl7fffltEbq4Arq6ukpaWptScO3dO2rVrJ5mZmc0OMSIiP/zwg0RGRopOp5OOHTvK3LlzZfv27WZdJ+bixYsCQLnOQ3PG5OTkJA8//LD4+/uLi4uLeHl5Sf/+/eVvf/ubyTViav34448ybtw40el04unpKcOHD5cjR47Uu5ypqakSEhIibm5uYjAYZN68eVJWVlZvrbe3t2zcuNEqPx8isq2W6LuWuH79usyaNUtCQkJEp9OJh4eH9OzZU+Lj4+XatWtKnSXXibFW3+3cubMAqPdR37Ls2rVLBg4cKO7u7uLj4yN/+MMf6r1gXlPYa99liLnF7SvTTz/9JADqJN6xY8fKH/7wBxER+fLLLwWAXL582aQmJCREXnvttRZf5jv597//LQAkPz9fRNQ9pqqqKvnoo4/Ezc1NvvvuO1WPhYhuYt+17zHZe99t88fENKb2JmiN3Za+uLgYbm5u8Pb2brDGVkQE8+fPx+DBg5UDu9Q4pvz8fHh5eUGj0WDWrFnIyMjAAw88oMqxEFHj1L5es++27lh4irUZzL0tvaU1LS02NhbHjx/Hvn376rympjH17NkTeXl5uHLlCrZu3YqpU6ciJydHeV1NYyEi86h1vWbfbVhLjIV7YhpRe32Axm5LbzAYUFlZiZKSkgZrbGHu3LnYtm0bsrOz0blzZ2W6Gsfk5uaG7t27o2/fvkhMTESfPn3w1ltvqXIsRNQ4Na/X7LutPxaGmEYEBQXBYDCY3Ja+srISOTk5ym3pa6/seGvNhQsXUFBQYJNb14sIYmNjkZ6ejj179iAoKMjkdTWO6XYigoqKCocYCxGZUuN6zb5rw7FY9QgbFSorK5Pc3FzJzc0VALJ69WrJzc2V06dPi8jNU8n0er2kp6dLfn6+TJ48ud5TyTp37iy7d++Wo0ePyuOPP26zU3hfeOEF0ev1snfvXrlw4YLy+P3335UaNY1p4cKF8tVXX8nJkyfl+PHjsmjRImnXrp3s2rVLdWMhopvYd+17TGrqu20+xGRnZ9d7+trUqVNF5OapcfHx8WIwGESj0ciQIUOUI85rlZeXS2xsrPj4+IiHh4dERUXJmTNnbDAaafB0vKSkJKVGTWN67rnnpGvXruLm5iYdO3aU4cOHKyuSiLrGQkQ3se/a95jU1HedRESsu2/HPtTU1OD8+fPQarU2P9CL1EtEUFZWhoCAALRrx29fiRrDvkvWYEnfddizk86fP1/vXT6JmqKoqMjkQD0iqot9l6zJnL7rsCFGq9UCuPmPoNPpbLw01OKuXQNq7/10/jzQvr1VZltaWorAwEDl94mIGmb1vttC6zXZN0v6rsOGmNpdmbU3sCIH5+z8n7/rdFZvdtw1TnRnVu+7Lbxek30zp+/yS34iIiJSJYYYIiIiUiWGGCIiUoVur2639SKQnWGIISIiu9RrSWa9fyeqxRBDDofNjoiobWCIISIiu8OvjsgcDDHkELj3hchxMMCQuRhiiIhINRhw6FYMMUREpCoMMlSLIYaIiIhUiSGGiIiIVIkhhoiIiFSJIYaIiOwGj3chSzDEkOrV1/TYCImIHB9DDBEREakSQwwREakO97YSwBBDRER2gsGELMUQQ0REqsTQQwwxREREpEoMMURERKRKDDFERESkSgwxREREpEoMMUREZHM8SJeagiGGHBabIhGRY2OIISIiIlViiCEiIptqzl5T7nFt2xhiiIhI1Rhk2i6GGCIiIlIlhhgiIiJSJYYYUjXuRiYiarsYYoiIiEiVGGLIoXFPDRGR42KIISIiIlViiCEiIiJVYoghIiKb4Ve+1BwMMURERKRKDDFERGQT3AtDzcUQQ0RERKrEEEOqxa04IqrFftA2McQQERGRKjHEEBERkSoxxBAREZEqWRRiEhMT0a9fP2i1Wvj5+WHcuHEoLCw0qRERJCQkICAgAB4eHggPD8d3331nUlNRUYG5c+eiQ4cOaN++PcaOHYuzZ8+a1JSUlCA6Ohp6vR56vR7R0dG4cuVK00ZJbRq/KycickwWhZicnBzMmTMHhw4dQlZWFqqqqhAZGYlr164pNStXrsTq1auxbt06HD58GAaDASNGjEBZWZlSExcXh4yMDKSlpWHfvn24evUqoqKiUF1drdRMmTIFeXl5yMzMRGZmJvLy8hAdHW2FIRMRqYejbjxy44KswaIQk5mZiWnTpuHBBx9Enz59kJSUhDNnzuDIkSMAbq5Ia9asweLFizFhwgQEBwfjww8/xO+//47U1FQAgNFoxPvvv4+//vWviIiIwMMPP4zNmzcjPz8fu3fvBgB8//33yMzMxMaNGxEWFoawsDC89957+OKLL+qsvEREjowbj0QNa9YxMUajEQDg4+MDADh58iSKi4sRGRmp1Gg0GgwdOhQHDhwAABw5cgQ3btwwqQkICEBwcLBSc/DgQej1egwYMECpGThwIPR6vVJzu4qKCpSWlpo8iIjUjhuP5uPenbanySFGRDB//nwMHjwYwcHBAIDi4mIAgL+/v0mtv7+/8lpxcTHc3Nzg7e3daI2fn1+dz/Tz81NqbpeYmKjsAtXr9QgMDGzq0IiI7BY3Hon+o8khJjY2FsePH8dHH31U5zUnJyeT5yJSZ9rtbq+pr76x+SxcuBBGo1F5FBUVmTMMIiLV4MYjkakmhZi5c+di27ZtyM7ORufOnZXpBoMBAOr8wl+8eFFZwQwGAyorK1FSUtJozS+//FLncy9dulRnRa2l0Wig0+lMHkREjoQbj0SmLAoxIoLY2Fikp6djz549CAoKMnk9KCgIBoMBWVlZyrTKykrk5ORg0KBBAIDQ0FC4urqa1Fy4cAEFBQVKTVhYGIxGI7799lul5ptvvoHRaFRqiIjaEm48mofHxbQtFoWYOXPmYPPmzUhNTYVWq0VxcTGKi4tRXl4O4GaKj4uLw/Lly5GRkYGCggJMmzYNnp6emDJlCgBAr9dj+vTpeOmll/Dll18iNzcXzzzzDHr37o2IiAgAQK9evTBq1CjMnDkThw4dwqFDhzBz5kxERUWhZ8+eVv4nICKyX4648cigQdbiYknxhg0bAADh4eEm05OSkjBt2jQAwMsvv4zy8nLMnj0bJSUlGDBgAHbt2gWtVqvUv/nmm3BxccHEiRNRXl6O4cOHIzk5Gc7OzkpNSkoK5s2bpxyINnbsWKxbt64pYyQHxCZIbcWcOXOQmpqKzz77TNl4BG5uEHp4eJhsPPbo0QM9evTA8uXLG9x49PX1hY+PDxYsWNDgxuM777wDAIiJieHGI9k1i0KMiNyxxsnJCQkJCUhISGiwxt3dHWvXrsXatWsbrPHx8cHmzZstWTwiIofDjUeihlkUYoiIqHVx45GoYbwBJLUJ/PqJyD5wXSRrYoghIiIiVWKIISIih8K9PW0HQwwRERGpEkMMERERqRJDDBEREakSQwypDr/vJiIigCGGiIhaCTdAyNoYYoiIyOEwMLUNDDFERESkSgwxRETU4rhnhFoCQwwRETkkBifHxxBDREREqsQQQ0RERKrEEENERESqxBBDbQa/HyciciwMMURERKRKDDFEROSwuAfWsTHEEBERkSoxxJCqcKuKSH243lJLYYghIiIiVWKIISIih8Y9QY6LIYaIiIhUiSGGiIiIVIkhhoiIWgy/yqGWxBBDbQobKhGR42CIISIih8cNGMfEEEOqwSZEpC5cZ6mlMcQQERGRKjHEUJvDrUOitonrvuNhiCEiIiJVYoghIiIiVWKIISKiNoNfKTkWhhgiIrI6hgVqDQwxpApsiETqERz/T1svArURDDFERNSmcKPIcTDEUJvEJkZEpH4MMURE1OZwQ8YxMMSQ3WOzISKi+jDEEBERkSoxxFCbxT08RETqxhBDREREqsQQQ3aNe0uIqKWwv6gfQwwREbVZDDLqxhBDREREqsQQQ20at8KIiNSLIYaIiNq0bq9u5waNStl9iFm/fj2CgoLg7u6O0NBQfP3117ZeJGolrdVU2LyITLXVvsteoD52HWK2bNmCuLg4LF68GLm5uXjssccwevRonDlzxtaLRkTkkNp632WQURe7DjGrV6/G9OnTMWPGDPTq1Qtr1qxBYGAgNmzYYOtFoxbW2o2Eu5OJbmLf/U8/YE+wfy62XoCGVFZW4siRI3j11VdNpkdGRuLAgQN16isqKlBRUaE8NxqNAIDS0tKWXVCyquD4fzbpfdWV11H7k66u+B01UtOk+dz++1L7XESaND8iNbFW362p+N0qy2Ot9bo5urz4MQqWjkRw/D9RsHRkq39+W2RJ37XbEPPrr7+iuroa/v7+JtP9/f1RXFxcpz4xMRFLly6tMz0wMLDFlpHsi772L+v/0PR5rKl/ellZGfR6ff0vEjkIa/XdcxumWW2ZrLFeN3sZ1pj+Sa3DnL5rtyGmlpOTk8lzEakzDQAWLlyI+fPnK89rampw+fJl+Pr61lvfFKWlpQgMDERRURF0Op1V5mlLHM+diQjKysoQEBBglfkRqQH7bsvheO7Mkr5rtyGmQ4cOcHZ2rpP+L168WGcrAQA0Gg00Go3JtLvuuqtFlk2n0znEL18tjqdx3ANDbQX7buvheBpnbt+12wN73dzcEBoaiqysLJPpWVlZGDRokI2WiojIcbHvktrY7Z4YAJg/fz6io6PRt29fhIWF4d1338WZM2cwa9YsWy8aEZFDYt8lNbHrEDNp0iT89ttvWLZsGS5cuIDg4GDs2LEDXbt2tcnyaDQaxMfH19l9qlYcDxHdjn23ZXE81uUkPHeUiIiIVMhuj4khIiIiagxDDBEREakSQwwRERGpEkMMERERqRJDDBEREalSmw8xX331FZ544gkEBATAyckJn376qcnrIoKEhAQEBATAw8MD4eHh+O6770xqKioqMHfuXHTo0AHt27fH2LFjcfbs2VYcxX8kJiaiX79+0Gq18PPzw7hx41BYWGhSo6YxbdiwASEhIcrVIMPCwrBz507ldTWNhYhuYt+17zGpqu9KG7djxw5ZvHixbN26VQBIRkaGyesrVqwQrVYrW7dulfz8fJk0aZJ06tRJSktLlZpZs2bJ3XffLVlZWXL06FEZNmyY9OnTR6qqqlp5NCIjR46UpKQkKSgokLy8PBkzZox06dJFrl69qsoxbdu2TbZv3y6FhYVSWFgoixYtEldXVykoKFDdWIjoJvZd+x6Tmvpumw8xt7p9ZaqpqRGDwSArVqxQpl2/fl30er28/fbbIiJy5coVcXV1lbS0NKXm3Llz0q5dO8nMzGy1ZW/IxYsXBYDk5OSIiGOMydvbWzZu3OgQYyFq69h31TEme+27bf7rpMacPHkSxcXFiIyMVKZpNBoMHToUBw4cAAAcOXIEN27cMKkJCAhAcHCwUmNLRqMRAODj4wNA3WOqrq5GWloarl27hrCwMFWPhYjq5wjrNftu642FIaYRtXdyvf3urf7+/sprxcXFcHNzg7e3d4M1tiIimD9/PgYPHozg4GAA6hxTfn4+vLy8oNFoMGvWLGRkZOCBBx5Q5ViIqHFqX6/Zd1t3LHZ97yR74eTkZPJcROpMu505NS0tNjYWx48fx759++q8pqYx9ezZE3l5ebhy5Qq2bt2KqVOnIicnR3ldTWMhIvOodb1m321YS4yFe2IaYTAYAKBOcrx48aKSQg0GAyorK1FSUtJgjS3MnTsX27ZtQ3Z2Njp37qxMV+OY3Nzc0L17d/Tt2xeJiYno06cP3nrrLVWOhYgap+b1mn239cfCENOIoKAgGAwGZGVlKdMqKyuRk5ODQYMGAQBCQ0Ph6upqUnPhwgUUFBQoNa1JRBAbG4v09HTs2bMHQUFBJq+rcUy3ExFUVFQ4xFiIyJQa12v2XRuOxaqHCatQWVmZ5ObmSm5urgCQ1atXS25urpw+fVpEbp5KptfrJT09XfLz82Xy5Mn1nkrWuXNn2b17txw9elQef/xxm53q98ILL4her5e9e/fKhQsXlMfvv/+u1KhpTAsXLpSvvvpKTp48KcePH5dFixZJu3btZNeuXaobCxHdxL5r32NSU99t8yEmOztbANR5TJ06VURunhoXHx8vBoNBNBqNDBkyRPLz803mUV5eLrGxseLj4yMeHh4SFRUlZ86cscFopN6xAJCkpCSlRk1jeu6556Rr167i5uYmHTt2lOHDhysrkoi6xkJEN7Hv2veY1NR3nURErLtvh4iIiKjl8ZgYIiIiUiWGGCIiIlIlhhgiIiJSJYYYIiIiUiWGGCIiIlIlhhgiIiJSJYYYIiIiUiWGGCIiIlIlhhgiIiJSJYYYIiIiUiWGGCIiIlKl/x912Xu/qWWBsgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_5\n",
    "mu = 100\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,1)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 100\")\n",
    "\n",
    "mu = 200\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,4)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 200\")\n",
    "\n",
    "mu = 300\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,7)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 300\")\n",
    "\n",
    "mu = 100\n",
    "si = 5\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,3)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"si = 5\")\n",
    "\n",
    "mu = 100\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,6)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"si = 10\")\n",
    "\n",
    "mu = 100\n",
    "si = 20\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,9)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"si = 20\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e16ff1f1",
   "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",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}