Random_numbers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assignment 4 - Random numbers\n",
    "Probability and Statistics<br>\n",
    "Autumn 2021<br>\n",
    "G01, Ahmed Al-Tuwaijari<br>\n",
    "[CC BY-NC-SA](https://creativecommons.org/licenses/by-nc-sa/4.0/),\n",
    "[Sakari Lukkarinen](https://peoplefinder.metropolia.fi/en/profile/8719/staff/Sakari-Lukkarinen)<br>\n",
    "[Helsinki Metropolia University of Applied Sciences](https://www.metropolia.fi/en/)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your own library import commands here\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1\n",
    "\n",
    "In this problem we play with *normally distributed* random number with *given* mean ($\\mu$) and standard deviation ($\\sigma$) and compare that to the *theoretical probability density function* of normal distribution.\n",
    "\n",
    "Coding:\n",
    "- Create an array of 500 [normally distributed](https://en.wikipedia.org/wiki/Normal_distribution) random numbers having a *mean* of 10.0 and *standard deviation* of 2.50.\n",
    "- Calculate the descriptive statistics for the array.\n",
    "- Create a [density histogram](https://matplotlib.org/3.2.1/api/_as_gen/matplotlib.pyplot.hist.html) of the values. Pay special attention to the bins settings.\n",
    "- Draw [vertical lines](https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.axvline.html) to show the range for $ \\mu \\pm 1.0 \\cdot \\sigma$.\n",
    "- Overlay a theoretical [probability density function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html) over the *density* histogram.\n",
    "- Count how many of the random values are between 10.0 and 15.0.\n",
    "- Calculate what is the *theoretical* probability that the random variable is between 10.0 and 15.0.\n",
    "\n",
    "Questions:\n",
    "- How much do the *given* mean value (10.0) and the *calculated* mean value (from descriptive statistics) differ from each other? Explain why.\n",
    "- Discuss how well does the *probability density function* fit to the histogram of randomly generated data?\n",
    "- What was the *counted* probability that the random values is between 10.0 and 15.0? How much that differ from the *theoretical* probability? Discuss about the difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/pv/18phz5dd1vb5vh9cqn3fkbx40000gn/T/ipykernel_51749/480613818.py:14: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"r-\" (-> color='r'). The keyword argument will take precedence.\n",
      "  ax.plot(x, rv1.pdf(x), 'r-', lw = 2, alpha=0.8, label = 'norm', color='black')\n"
     ]
    },
    {
     "data": {
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BT5nZh5ImSJoAIKmHpDXAd4AfSFojqQDoDrwl6X3g38CLZvZysOrbgTMkLQPOCKadazIVxZvY+X7869jhxHFkZO/fDZmNld19IHlDTgIzdsx8ErNYJHE4V59Qxzozs0KgsNq8KQmfNxA/pVZdMXB4LevcApyWwjCdS5qZUfzvaRCrJHfgMbQ9cHCk8bQ/4hz2rlpA+aerKVnyDu2GnBRpPM7VxEcGcK4BSj9ZSOnaRSg7l/ZHnRd1OGRk51Bw7EUA7Jz/ApV7iiOOyLnP80TjXJKsoizemgHajxhNZm77iCOKy+k7nLa9hmLle9n5bmH9FZxrYp5onEvSrg/foHL3NrI69SJvyIlRh7OPJAqOvgCUwZ5lsynfujbqkJz7DE80ziWhcs9Odn/wdwAKjr4QKb3+62R16Ebe4BMBo3judB+exqWV9Prf4lya2rXgFayilLa9h9G2x8FRh1Oj9iNGoexcytYvoXTt4qjDcW4fTzTO1aOieBMlS94BKS06ANQmo2078oefCcDOuc95d2eXNjzROFePnfMLwWLkDjyGNh17RB1OndoNOYnM/E5U7NjA3qJ5UYfjHOCJxrk6lW9Zw95V76GMLNqPODvqcOqlzDbkDz8LgJ3vv4LFKiOOyDlPNM7VqWoEgLwhJ5HZrmO0wSQpd+BIMtt3oXLnp+xZMbf+Cs6FzBONc7Uo37qW0k8+QBlZtDvsy1GHkzRlZNL+8HirZteCVygv96dxumh5onGuFlWjIucNPpHM3IKIo2mYnAFHkVXQjcpdW3n++eejDse1cp5onKtB+da17F29oNm1ZqpIGeSPGAXAH//4Ryoq/Jk1LjqeaJyrQVVrJveQE8jM6xBxNPsnp98IMgu6sn79embMmBF1OK4V80TjXDXl2zfsa83kf6H5DhQuZZB/2OkAPPzww8Rifl+Ni0aojwlwrjmqGmomd9CxobVm+jXwQWn7K3fAUXTbM5eioiLeeustvvjFBj0R3bmU8BaNcwkqd29nT9E8kGg39NSow2k0ZWZx+eWXA/FrNT4GmouCJxrnEuxe9E+wSnL6DieroEvU4aTEhRdeSEFBAQsXLmT+/PlRh+NaIU80zgViZXspWfoOAO2GNb+eZrXJzc1l7NixQPxajXNNzRONc4GSpe9g5XvJ7j6Q7K4HRR1OSo0dO5acnBxmzpxJUVFR1OG4VibURCNplKQlkpZLmljD8iGSZkoqlXRTwvw+kt6QtEjSh5K+mbBskqS1kt4LXqPD3AfXOpSXl7N70ZsAzfK+mfoUFBRw7rnnAvD4449HHI1rbUJLNJIygcnA2cBQYJykodWKbQVuBO6qNr8C+K6ZHQocB1xfre49ZjYiePmza12jzZgxg1jJDrI69KBtr0OjDicU48aNA6CwsJBt27ZFHI1rTcJs0RwDLDezIjMrA54AxiQWMLNNZjYHKK82f72ZzQ8+7wQWAb1CjNW1YmbGY489BkC7Yaem3dMzU+Wggw7ipJNOoqysjGeffTbqcFwrEub/qF7AJwnTa9iPZCGpH3AEMDth9g2SFkiaKumAWupdK2mupLmbN29u6GZdK/Luu++ydOlSMnLakzvgyKjDCdVll10GwNNPP01ZWVnE0bjWIsxEoxrmNagTv6R84FngW2ZWHMy+DxgIjADWA3fXVNfMHjCzkWY2smvXrg3ZrGtlnnzySQDyDjkeZbaJOJpwHX300QwaNIgtW7bw6quvRh2OayXCHBlgDdAnYbo3sC7ZypLaEE8yj5nZX6vmm9nGhDIPAi80PlTX0jw+e/W+z/9Xx134lbu3senZaYDodvwJTRBZtCQxbtw4fvrTn/LYY48xevRopJr+JnQudcJs0cwBBknqLykbGAtMT6ai4t/8PwCLzOxX1Zb1TJi8EPggRfG6VqhkydtgRs5BhzebB5s11qhRo+jUqRNLly71Gzhdkwgt0ZhZBXAD8Arxi/lPmdmHkiZImgAgqYekNcB3gB9IWiOpADgRuAL4cg3dmO+UtFDSAuBU4Nth7YNr2ayi/D83aB7aesYAy87O5pJLLgHgqaeeijga1xqEOqhm0PW4sNq8KQmfNxA/pVbdW9R8jQczuyKVMbrWa8/H84mVltCmU2/adO0XdTihqWkAz8qSfDat28nCR6fxeMnwz7XmVt5+ThNF51qDltmP07l6mBm7F/8TgLxDv9jqrlNk5nUgp+9wMKNk2cyow3EtnCca1yqVb/qYiq1ryWjbjtz+R0QdTiTyhpwEQMmSd7BKfwKnC48nGtcq7WvNHHJCi+/SXJvs7gPJ6tCD2N6d7F29MOpwXAvmica1OpUlO9i76n2QyBt8YtThREZSQqvmrYijcS2ZJxrX6pQsmx3v0tznC62mS3NtcgeMRFltKdu4gvJtSd/m5lyDJJVoJJ2rljoAlGtVzGLsCS5+5x3S8m/QrE9Gdg65A48GoGSxt2pcOJJNHmOBZZLulNQyh7Z1rULp2sVU7t5GZn5nsg88JOpw0kLV6bM9RXOJle2JOBrXEiWVaMzscuIDW64A/hg8Q+ZaSe1Djc65FCtZ8jYQjGvmjXQA2nTsQXb3g7GKMvasmBN1OK4FSvp/WjCo5bPEh/vvSXz4l/mS/jek2JxLqcrd2yld+xEog9yDj406nLTyma7O1qCxb52rV7LXaM6XNA34O9AGOMbMzgYOB26qs7JzaaJk2ax4J4C+w8nM9cZ4opy+XyAjpz0VOzZQvvnjqMNxLUyyLZpLiD/VcriZ/dLMNgGYWQnwtdCicy5FLFa57w74vEOOjzia9KOMTHIPPgaIt2qcS6VkE816M/tn4gxJdwCY2espj8q5FCtdu4hYyQ4y23chu+egqMNJS1UJeO/K9yguLq6ntHPJSzbRnFHDvLNTGYhzYar6K907AdQuq30X2h44GItV8OKLtT/Dx7mGqvN/nKTrJC0EhgSPTq56fQwsaJoQnWucyl3bKF23CDIyvRNAPXKDe4v++te/eqcAlzL1PSbgceAl4BfAxIT5O81sa2hROZdCJctmBg83G05mTn7U4aS1nD6HkZHTno8//pj333+fEVEH5FqE+s4hmJmtBK4Hdia8kNQp3NCcazwziw85A616XLNkKSOTvEHHAfFWjXOpUF+ieTx4nwfMDd7nJUw7l9Yqd28ltmcHWQXdyO4+MOpwmoXcQcchiddee43SsrKow3EtQJ2JxszODd77m9mA4L3qNaBpQnRu/1Xs2AhA7iHHt7qHm+2vrPadOe644ygrK2P16tVRh+NagGRv2DxRUrvg8+WSfiWpbxL1RklaImm5pIk1LB8SDGdTKummZOpK6iTpVUnLgvcDktkH1/rEyvcS270dZWSRF9wj4pJz0UUXAfDxxx97pwDXaMn287wPKJF0OHAzsAp4tK4KkjKBycS7QQ8FxkkaWq3YVuBG4K4G1J0IvG5mg4DX+WwnBef2qdixCYCcgw4no227iKNpXk4++WQ6d+7Mrp07+XTLlqjDcc1csommwuJ/1owBfmNmvwHqG8PjGGC5mRWZWRnxMdLGJBYws01mNgcob0DdMcCfgs9/Ai5Ich9cK2Jm+06b5Q32xwE0VFZWFmPGxP/LrfzYh6RxjZNsotkp6fvA5cCLQYujvuff9gI+SZheE8xLRl11u5vZeoDgvVtNKwhGl54rae7mzZuT3KxrKSp3b4XKcpSdS5tufjlxf1xwwQUArF271jsFuEZJNtF8BSgFrjGzDcR/9H9ZT52arrwme7K3MXXjhc0eMLORZjaya9euDanqWoCK7fHWTFaH7t4JYD8deOCBdO/enVgsxupVq6IOxzVjyT6PZoOZ/crM/hVMrzazR+qptgbokzDdG0j2WbF11d0oqSdA8L4pyXW6VmLX7t3ESraDMsgqqLHB65LUv39/wDsFuMZJttfZRUEvrx2SiiXtlFTfqHtzgEGS+kvKJv6UzulJxlVX3enA+ODzeOC5JNfpWomPg2sKme07o8z6Br9wdenRsyc5OTns2rXLOwW4/Zbs/8I7gfPMbFGyKzazCkk3AK8AmcBUM/tQ0oRg+RRJPYjf+FkAxCR9CxhqZsU11Q1WfTvwlKRrgNXApcnG5Fq+8vJyVgWnebI69Ig4muYvQ+Kgfv1YsngxHxcV4Seh3f5INtFsbEiSqWJmhUBhtXlTEj5vIH5aLKm6wfwtwGkNjcW1Dm+88QZlpaWobR4ZuT6uWSr0CxLNunXr2L59Ox07dow6JNfMJNsZYK6kJyWNC06jXSTpolAjc24/VI3PldWhO6qxT4lrqHZ5eXTv0YNYLMbzzz8fdTiuGUo20RQAJcCZwHnB69ywgnJuf6xevZq5c+eSmZlJVoGf5EmlAUGngGnTphGLxSKOxjU3SZ06M7Orww7Eucaqas307t2bJRXeCSCVuvfoQU5u7r5kfswxPqSPS16yvc4OkfS6pA+C6eGSfhBuaM4lr6ysbN9pnf4D/AbNVMuQ6N+vH+CPD3ANl+ypsweB7xMMFWNmC4h3OXYuLfz9739nx44dDB48mAP8YnUo+vXrR0ZGBm+88QZbt/pzD13ykk00eWb272rzKlIdjHP769lnnwXg4osv9pEAQpKbm8vJJ59MZWUl06cne0ucc8knmk8lDSQYBkbSJcD60KJyrgGKiop49913ycvLY9SoUVGH06JdfPHFQPz0mXcKcMlKNtFcD9wPDJG0FvgWMCGsoJxriGnTpgEwatQo8vLyIo6mZTvuuOPo2bMn69atY/bs2VGH45qJOhONpO9I+g7xofgLgduAKcBfgYtDj865epSWlvLCCy8A//lr24UnIyODCy+8EPBOAS559bVo2gevkcB1wAFAR+KtmeoPMXOuyb366qvs3LmToUOHMnjw4KjDaRXOP/98MjMzefPNN/FHcLhk1HmzgZn9BEDSDOBIM9sZTE8Cng49OufqUfVXtbdmUqvfxBcB+Pns1Z+Z/3/B/G30Zu8nCxhy5c9of/hZAKy8/ZymDdI1G8leo+kLJD75qAzol/JonGuAZcuWsWDBAtq1a8eZZ54ZdTitSt7gEwHYs3QmZt4pwNUt2dunHwX+LWka8Z5nF/Kfxyk7F4mq1sw555xDbm5uxNG0Ltk9B5GZ35nKXVsoXbuInN7Dog7JpbFkH3x2G3A1sA3YDlxtZr8IMS7n6lRSUsKLL8ZP41x0kY/v2tSkDPIGnwBAyZJ3Io7GpbukB4Qys/nA/BBjcS5pM2bMoKSkhOHDh3PwwQdHHU6rlDvwGHbOL6R07UdU7t4WdTgujSV7jca5tOKdAKKXmduenIOGgxkly2ZFHY5LY55oXLOzePFiPvroIwoKCjj99NOjDqdVq+oUULJ0FpWVlRFH49KVJxrX7Dz9dLxn/TnnnEPbtm0jjqZ1y+4+kKyCbsT27OCtt96KOhyXpkJ9aIekUcBvgEzgITO7vdpyBctHE3+w2lVmNl/SYODJhKIDgB+Z2a+De3j+G6i6U+z/gsc+uxao6n6OKrHSEjY99TgWq2DDik78ttpy+Py9Hy48ksg95Hh2zn2OZ599li996UtRh+TSUGgtGkmZwGTgbOKjCIyTVH00gbOBQcHrWuA+ADNbYmYjzGwEcBTxJDQtod49Vcs9ybQuJctmYbEK2h44mKyCblGH44C8g49BGVnMnDmTTz75JOpwXBoK89TZMcByMysyszLgCWBMtTJjgEcsbhbQUVLPamVOA1aY2aoQY3XNgFmMkiVvA5A35OSIo3FVMtq2I2fAUZjZvtOaziUKM9H0AhL/vFkTzGtombHAX6rNu0HSAklTJR1Q08YlXStprqS5Ph5Ty1C6dhGVu7aQmd+Jtr19qL100m7ISQBMnz6dkpKSiKNx6SbMRFPT06esIWUkZQPn89lx1e4DBgIjiD8T5+6aNm5mD5jZSDMb2bVr1waE7dJVyeL4xea8wScieT+WdNKmcx+GDx/Orl27eOmll6IOx6WZMP+3rgH6JEz3BtY1sMzZwHwz21g1w8w2mlmlxQdYepD4KTrXwlUUb6J07SKUkUXeoOOiDsfVYOzY+NPdn3zyScyq/03pWrMwE80cYJCk/kHLZCxQ/fmv04ErFXccsMPMEp/cOY5qp82qXcO5EPgg9aG7dFOyOH5tJmfAUWS0bRdxNK4mX/7yl+nSpQtFRUXMmzcv6nBcGgkt0ZhZBXAD8AqwCHjKzD6UNEFS1dM5C4EiYDnx1sk3qupLygPOIP6QtUR3SlooaQFwKvDtsPbBpYdYeSkly+NPc6y6FuDST1ZW1r6RGp588sl6SrvWJNT7aIKux4XV5k1J+GzEHxNdU90SoHMN869IcZguze0tmoeV76VN13606dyn/gouMhdddBF/+MMfePPNN1m/fj09e1bvROpaI7+i6tKambF78b8AaOddmtNe586dOf3004nFYjzzzDNRh+PShCcal9bKNiynYvt6MnKCARxd2vvKV74CwN/+9jdKS0sjjsalg1BPnTmXqPpwMsnY/dE/gKBLc2abFEfkwnDYYYdx6KGHsmjRIl555RXOP//8qENyEfMWjUtbFcWbKF3zYbxLczBKsEt/kvZ1dX788ce9q7PzROPS1+6P/glAzsCRZOa2jzga1xBnnHEGnTt3Zvny5cyePTvqcFzEPNG4tBQrLWHP8n8D0G7oKdEG4xosOzt737Waxx57LOJoXNQ80bi0VLL0HayyjLYHDqFNxx5Rh+P2wyWXXEJOTg4zZ85kxYoVUYfjIuSJxqUdq6xg96KgS7O3ZpqtgoKCfR0BvFXTunmicWln78r3iO3ZQVaHHmQfODjqcFwjjBs3Dkm89NJLbNmyJepwXEQ80bi0Ymb7ujS3G3YK8YewuuaqT58+nHLKKZSXl/uwNK2YJxqXVsrWL6V86xoyctqTO+CoqMNxKXD55ZcD8Mwzz7Bnz56Io3FR8ETj0squha8B0O7QL/oNmi3E8OHDOeywwyguLub555+POhwXAU80Lm2UbV5F2YZlKKut36DZgkjiyiuvBOCRRx6hoqIi4ohcU/NE49LG7g9eByBvyElktM2LOBqXSqeccgr9+vVjw4YNFBYW1l/BtSieaFxaKN++gb2rF6CMLNoN/VLU4bgUy8jI4Oqrrwbg4YcfJhaLRRyRa0qeaFxaqGrN5B58DJm5BRFH48Jw1llnceCBB7J69Wpef/31qMNxTcgTjYtc5a5t7CmaBxLthn056nBcSLKyshg/fjwAf/zjH32wzVbEE42L3K4PXweLkdPvCLIKukQdjgvReeedR5cuXVi6dClvvfVW1OG4JhJqopE0StISScslTaxhuSTdGyxfIOnIhGUrJS2U9J6kuQnzO0l6VdKy4P2AMPfBhaty9zZKls4ERP4Xzog6HBey7OzsfffVTJ061Vs1rURoiUZSJjAZOBsYCoyTNLRasbOBQcHrWuC+astPNbMRZjYyYd5E4HUzGwS8Hky7ZmrXwtcgVklOv8Npc4A/X741uOiiiygoKGDhwoXMmTMn6nBcEwizRXMMsNzMisysDHgCGFOtzBjgEYubBXSUVN+vzRjgT8HnPwEXpDBm14Qqd22jZOksQOQfPirqcFwTycvL29eqmTJlirdqWoEwE00v4JOE6TXBvGTLGDBD0jxJ1yaU6W5m6wGC9241bVzStZLmSpq7efPmRuyGC8uuha+CVZLT/wh/FEArM3bsWDp06MCCBQuYOXNm1OG4kIWZaGoaDbH6ny51lTnRzI4kfnrteklfbMjGzewBMxtpZiO7du3akKquCVTs2krJstkg0f7ws6IOxzWxvLw8rrrqKgB+//vfe6umhQsz0awB+iRM9wbWJVvGzKreNwHTiJ+KA9hYdXoteN+U8shd6HYviLdmcvsdSVaH7lGH4yJw6aWX0rlzZxYvXswbb7wRdTguRGEmmjnAIEn9JWUDY4Hp1cpMB64Mep8dB+wws/WS2klqDyCpHXAm8EFCnfHB5/HAcyHugwtBRfEmSpbHWzP5I7w101rl5ORwzTXXAPFrNT5aQMsVWqIxswrgBuAVYBHwlJl9KGmCpAlBsUKgCFgOPAh8I5jfHXhL0vvAv4EXzezlYNntwBmSlgFnBNOuGdk5vxAsRu7AY8gqqPESm2slLrjgAnr06EFRUREzZsyIOhwXkqwwV25mhcSTSeK8KQmfDbi+hnpFwOG1rHMLcFpqI3VNpWzzKvaueg9lZNF+xNlRh+Milp2dzX//93/zs5/9jClTpnDaaafRpo0/HqKlCTXROJfIzNg5L/48kryhXyKzXcdoA3Ip1W/ii/tVb8Vt5/LII4+watUqnnnmGcaNG5fiyFzUfAga12RK1y6ibONylJ1H/mHeKHVxmZmZfPOb3wTgwQcfpLi4OOKIXKp5onFNIhaL7WvN5A8/w5834z7j5JNP5qijjqK4uJipU6dGHY5LMU80rkn87W9/o2L7ejLbHUC7ISdFHY5LM5L49re/DcCTTz7J2rVrI47IpZInGhe64uJiJk+eDED7kWNQpl/sdZ83ZMgQRo8eTXl5Ob/73e+iDselkCcaF7r777+fHTt2kN19IDkH1diZ0DkArr/+erKzs3n11VeZN29e1OG4FPFE40K1YsUKnn76aTIyMig45iKkmkYdci6ue/fufO1rXwPgjjvuoKKiIuKIXCp4onGhMTPuuusuYrEYF198MW06VR9T1bnPu/LKK+nduzdFRUU88cQTUYfjUsDvo3H7JZl7JvZ8PJ/t/3wNZeexaUN/Mto2QWCu2cvOzubmm2/mxhtv5IEHHuDMM8+kWzcfQaI58xaNC0WstITif08DoODIc8lo2y7iiFxzcsIJJ3DqqadSUlLCr3/966jDcY3kicaFonjuc8T27iS72wByDzku6nBcM/Sd73yHtm3bMmPGDN5+++2ow3GN4InGpVzp+mXsWT4bMjLpcMJXkPxr5hquZ8+eXHfddQDcdttt7Nq1K+KI3P7yXwCXUlZRzo6ZTwKQP/xMf9aMa5TLLruMYcOGsWnTJn7zm99EHY7bT94ZwKXUzndfpHLnp2R16OHjmbmk1NexpDz3i3y6fjYLf/cwv1uSS9sDB7Py9nOaKDqXCt6icSlTun4puz/6B0h0OHEcyvS/Y1zjtenYY9/jvne88wSx8r0RR+QayhONS4lYaQnb33oMgPzhZ5Hd9aCII3ItSbvDTqNNp95U7t5G8axnow7HNZAnGpcSO2Y/S6xkB2269CV/+BlRh+NaGGVk0uHky1FmG/YUzeHll1+uv5JLG55oXKPtKZrH3o/nocxsOp58OcrIjDok1wK16diDgqMvBODnP/+5j/DcjISaaCSNkrRE0nJJE2tYLkn3BssXSDoymN9H0huSFkn6UNI3E+pMkrRW0nvBa3SY++DqVr59w75eZgVHX0BWgd/B7cKTe8jx5PQdTklJCbfccouPhdZMhJZoJGUCk4GzgaHAOElDqxU7GxgUvK4F7gvmVwDfNbNDgeOA66vVvcfMRgSvwrD2wdUtVl7K9n88jFWUkdP/SHIPOT7qkFwLJ4kOJ4ylW7dufPDBB9x7771Rh+SSEGaL5hhguZkVmVkZ8AQwplqZMcAjFjcL6Cipp5mtN7P5AGa2E1gE+IiMacTMKJ71NBU7NpDVoTsdjv8vH5nZNYmMtnn84he/IDMzk8cff5zCQv9bM92FmWh6AZ8kTK/h88mi3jKS+gFHALMTZt8QnGqbKumAlEXsklay6E32FM2NX5c55Woy2uREHZJrRQ4//HC+973vAXDrrbeyZMmSiCNydQkz0dT05601pIykfOBZ4FtmVhzMvg8YCIwA1gN317hx6VpJcyXN3bx5cwNDd3V5++23KZ77HAAdThxHm449Io7ItUYXX3wx559/PmVlZdx0001s27Yt6pBcLcJMNGuAPgnTvYF1yZaR1IZ4knnMzP5aVcDMNppZpZnFgAeJn6L7HDN7wMxGmtnIrl27NnpnXNyKFSv4/ve/D2bkHz6K3P5HRB2Sa6UkMXHiRIYNG8b69ev57ne/S2lpadRhuRqEeev2HGCQpP7AWmAscFm1MtOJnwZ7AjgW2GFm6xU/2f8HYJGZ/SqxQtU1nGDyQuCDEPehxUvmuTJVKndvZ8tLv6Fy9zZy+h1BfnC3tnNRyc7O5q677uKqq65iwYIF3HLLLdx5551kZPidG+kktH8NM6sAbgBeIX4x/ykz+1DSBEkTgmKFQBGwnHjr5BvB/BOBK4Av19CN+U5JCyUtAE4Fvh3WPrj/iJWWsPXVKVTu3kabLgfR8cTL/OK/Swtdu3blt7/9Le3bt+cf//gHd911F2bVz9K7KIU6GFXQ9biw2rwpCZ8NuL6Gem9R8/UbzOyKFIfp6hEr38vW1+4Pepj1oNPp16KsNlGH5dw+AwYM4O677+b666/nqaeeIj8/n+uuu87/GEoT3r50dYqVl7Lt7w9R/ukqMtsdQKczJvjTMl1aOvLII7ntttvIyMhg6tSpPPTQQ1GH5AKeaFytYuV72fb6A5RtWE5GTns6nXkdme06Rh2Wc7X68pe/zK233kpGRgb3338/U6dOjTokhycaV4tY2R62vjqFso0ryMjrQOez/9eHl3HNwplnnsmkSZOQxO9//3vuvfdev2YTMU807nPivcvupXzzSjLbHUDnszzJuOZl9OjR3HrrrWRmZvLII4/ws5/9jMrKyqjDarU80bjPKN+6lk8L76Fi+3qyCrrRadT/klXQJeqwnGuws846i3vuuYe2bdsyffp0vvOd77Br166ow2qVPNG4ffauXsCWl+4lVrKD7G4D6Dz6W2Tld4o6LOf22wknnMB9991HQUEBb7/9NldddRWrV6+OOqxWxxONwyxG8bzn2fbGVKyilJx+R9DpzOvIaJsXdWjONdrw4cN59NFHGThwICtXrmT8+PG88847UYfVqniiaeUqd29j64zfs/uD10Gi/cgxdPzilSjT75NxLUevXr344x//yCmnnMLOnTu58cYb+dWvfkVZWVnUobUKnmhaKTOjsLCQzc/dkdB9+Xryh53qN7m5FikvL48777yT66+/ft8jBsaPH09RUVHUobV4nmhaoR07djBx4kR+9KMfYeV7advnMLqcfzNtexwcdWjOhSojI4Orr76aqVOn0rt3b5YtW8bll1/Oww8/TCwWizq8FssTTStUVlbGnDlzyMvLo8MJ4zjg1GvIzG0fdVjONZlhw4bx+OOPM2bMGMrKypg/f7635EMU6lhnrmk1ZCTm0t7nktm+C3ntO4cYkXPhaMh3vW5HUnpoHtOsO9O/X/OTOlfefk6KttV6eaJppdoeODjqEJxLC217DYk6hBbPT50555wLlbdonHOuDvtzms5Pt32Wt2icc86FyhONc865UHmicc45F6pQE42kUZKWSFouaWINyyXp3mD5AklH1ldXUidJr0paFrwfEOY+OOeca5zQOgNIygQmA2cAa4A5kqab2UcJxc4GBgWvY4H7gGPrqTsReN3Mbg8S0ETg/4W1H84511D7e5/P/nQiaA6dFcJs0RwDLDezIjMrA54AxlQrMwZ4xOJmAR0l9ayn7hjgT8HnPwEXhLgPzjnnGinMRNML+CRhek0wL5kyddXtbmbrAYJ3f/Sjc86lsTDvo6lp4KDqD+6urUwydeveuHQtcG0wWSrpg4bUj0gX4NOog0hCWsf51f98jMf5/suRxZIEP5apldbHM0GNceqOptl4A7aTkiFEwkw0a4A+CdO9gXVJlsmuo+5GST3NbH1wmm1TTRs3sweABwAkzTWzkfu7I03F40yt5hBnc4gRPM5Ua05xpmI9YZ46mwMMktRfUjYwFphercx04Mqg99lxwI7gdFhddacD44PP44HnQtwH55xzjRRai8bMKiTdALwCZAJTzexDSROC5VOAQmA0sBwoAa6uq26w6tuBpyRdA6wGLg1rH5xzzjVeqGOdmVkh8WSSOG9KwmcDrk+2bjB/C3BaA0N5oIHlo+JxplZziLM5xAgeZ6q1qjgV/613zjnnwuFD0DjnnAtVi0o0jRnypglj7CPpDUmLJH0o6Zs1lDlF0g5J7wWvH0UQ50pJC4Ptf67nSZocy8EJx+g9ScWSvlWtTCTHUtJUSZsSu9UnO3xSfd/jJojzl5IWB/+u0yR1rKVund+RJohzkqS1Cf+2o2upG/XxfDIhxpWS3qulbpMcz9p+g0L9fppZi3gR7zSwAhhAvHv0+8DQamVGAy8Rv0/nOGB2BHH2BI4MPrcHltYQ5ynACxEfz5VAlzqWR34sa/j33wAclA7HEvgicCTwQcK8O4GJweeJwB217Eed3+MmiPNMICv4fEdNcSbzHWmCOCcBNyXxvYj0eFZbfjfwoyiPZ22/QWF+P1tSi6YxQ940GTNbb2bzg887gUV8fsSE5iDyY1nNacAKM1sVYQz7mNk/ga3VZiczfFIy3+NQ4zSzGWZWEUzOIn4fW6RqOZ7JiPx4VpEk4L+Av4S1/WTU8RsU2vezJSWaxgx5EwlJ/YAjgNk1LD5e0vuSXpI0rGkjA+IjMcyQNE/xURaqS6tjSfxeq9r+A0d9LKskM3xSuh3XrxFvudakvu9IU7ghOMU3tZZTPel0PE8GNprZslqWN/nxrPYbFNr3syUlmsYMedPkJOUDzwLfMrPiaovnEz8FdDjwW+BvTRwewIlmdiTxEbavl/TFasvT6VhmA+cDT9ewOB2OZUOk03G9BagAHqulSH3fkbDdBwwERgDriZ+Wqi5tjicwjrpbM016POv5Daq1Wg3z6j2eLSnRNGbImyYlqQ3xf+DHzOyv1ZebWbGZ7Qo+FwJtJHVpyhjNbF3wvgmYRrzJnCgtjmXgbGC+mW2sviAdjmWCjVWnF1X78ElpcVwljQfOBb5qwcn56pL4joTKzDaaWaWZxYAHa9l+uhzPLOAi4MnayjTl8azlNyi072dLSjSNGfKmyQTnaf8ALDKzX9VSpkdQDknHEP932tKEMbaT1L7qM/GLw9UHJY38WCao9S/FqI9lNckMn5TM9zhUkkYRf8bT+WZWUkuZZL4joap2TfDCWrYf+fEMnA4sNrM1NS1syuNZx29QeN/PsHs4NOWLeE+opcR7RdwSzJsATAg+i/gD1VYAC4GREcR4EvGm5gLgveA1ulqcNwAfEu/RMQs4oYljHBBs+/0gjrQ8lkEcecQTR4eEeZEfS+KJbz1QTvyvwGuAzsDrwLLgvVNQ9kCgsK7vcRPHuZz4efiq7+eU6nHW9h1p4jgfDb57C4j/2PVMx+MZzH+46juZUDaS41nHb1Bo308fGcA551yoWtKpM+ecc2nIE41zzrlQeaJxzjkXKk80zjnnQuWJxjnnXKg80TjXhCTtijoG55qaJxrnnHOh8kTjXCNIukPSNxKmJ0n6saTXJc0Pni/yudFtFX9OzgsJ07+TdFXw+ShJbwaDK76SMCzIjZI+CgaRfKIJds+5lMiKOgDnmrkngF8Dvw+m/wsYBdxjZsXBuGqzJE23JO6ODsag+i0wxsw2S/oKcBvxUZQnAv3NrFS1PIzMuXTkica5RjCzdyV1k3Qg0BXYRnwIknuC0XdjxIdR7078wWz1GQwcBrwaDNGWGawP4kOGPCbpb6T/KNTO7eOJxrnGewa4BOhBvIXzVeJJ5ygzK5e0EsipVqeCz566rlou4EMzO76G7ZxD/AmO5wM/lDTM/vOAMufSll+jca7xniA+iu0lxJNOB2BTkGROBQ6qoc4qYKiktpI6EH9CKMASoKuk4yF+Kk3SMEkZQB8zewO4GegI5Ie5U86lirdonGskM/swGOJ9rZmtl/QY8LykucRHxl1cQ51PJD1F/HTYMuDdYH6ZpEuAe4MElEX8GtBS4M/BPBG/BrQ99J1zLgV89GbnnHOh8lNnzjnnQuWJxjnnXKg80TjnnAuVJxrnnHOh8kTjnHMuVJ5onHPOhcoTjXPOuVB5onHOOReq/w9N7Dy3AzkRtAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Amount of values between 10 and 15 is:  222\n",
      "Probability of random value being between 10 and 15:  0.444\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>9.830321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.507310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>3.461789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>8.161782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>9.762490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>11.476371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>19.439205</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0\n",
       "count  500.000000\n",
       "mean     9.830321\n",
       "std      2.507310\n",
       "min      3.461789\n",
       "25%      8.161782\n",
       "50%      9.762490\n",
       "75%     11.476371\n",
       "max     19.439205"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your code\n",
    "mu = 10.0\n",
    "sigma = 2.5\n",
    "data = np.random.randn(500) * sigma + mu\n",
    "\n",
    "line1 = mu + 1.0 * sigma\n",
    "line2 = mu - 1.0 * sigma\n",
    "\n",
    "rv0 = norm()\n",
    "rv1=norm(loc = mu, scale = sigma)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "mean, var, skew, kurt = rv1.stats(moments='mvsk')\n",
    "x = np.linspace(rv1.ppf(0.01), rv1.ppf(0.99), 500)\n",
    "ax.plot(x, rv1.pdf(x), 'r-', lw = 2, alpha=0.8, label = 'norm', color='black')\n",
    "vals = norm.ppf([0.001, 0.5, 0.999])\n",
    "np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))\n",
    "\n",
    "plt.hist(data, density = True, bins = 20)\n",
    "plt.axis([0,20,0,0.2])\n",
    "plt.suptitle('Density histogram')\n",
    "plt.xlabel('values')\n",
    "plt.ylabel('density')\n",
    "plt.axvline(x = line1, color= 'red', lw=4, alpha = 0.6)\n",
    "plt.axvline(x = line2, color= 'red', lw=4, alpha = 0.6)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "between = ((10 <= data) & (data <= 15)).sum()\n",
    "print(\"Amount of values between 10 and 15 is: \", between)\n",
    "print(\"Probability of random value being between 10 and 15: \", between/500)\n",
    "\n",
    "dframe = pd.DataFrame(data)\n",
    "dframe.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answers:**\n",
    "\n",
    "a) Typically the difference is up to $\\pm$ 0.2. The answer as to why, probably lies within the randomness of how the numbers are generated. If you increase the sample sizefrom 500 though, the accuracy will drastically improve.\n",
    "\n",
    "b)They match very clearly although the generated numbers do tend to spike up or fall short of the probability density function at certain points. Again, if you were to increase the number of values to say 10000, and the bins to 35, we would a histogram almost perfectly fitting the function.\n",
    "\n",
    "c)The counted probability is is between 10.0 and 15.0 is 0.462. According to normal distribution formula. The resulut for f(10) and f(15) is 0.0128 and 1.773x10^-13, respectively(the difference is 0.0128). I can see the counted probability is bigger than theoretical probability is 0.4492. I think it has  a difference because we may use different conclusion forms or may use different methods for predicting the probability.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Problem 2\n",
    "\n",
    "The aim of this problem is to learn to use [exponential distribution](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.expon.html) from [scipy.stats](https://docs.scipy.org/doc/scipy/reference/stats.html) library. We use the values given in YouTube video [Example distribution - Example 1](https://www.youtube.com/watch?v=4PEX-SuftjQ).\n",
    "\n",
    "Coding:\n",
    "- Create an array `x2` of 2 000 [exponentially distributed](https://en.wikipedia.org/wiki/Exponential_distribution) random numbers having the parameter value $\\lambda$ given in the Youtube video. This array simulates the real data.\n",
    "   - Note: Read carefully the notes of `scipy.stats.expon` function and find out how to convert $\\lambda$ to *scale*.\n",
    "- Calculate the descriptive statistics for the simulated data.\n",
    "- Draw a histogram of the values. (Remember to tune the bin settings properly).\n",
    "- Draw also a [boxplot](https://en.wikipedia.org/wiki/Box_plot) of the values.\n",
    "- Using the *percent point function* (see scipy.stats.expon) find the probability $P(2 < x < 4)$. \n",
    "- Count the proportion of the values in the simulated data are between 2 and 4.\n",
    "\n",
    "Questions:\n",
    "- What are the values for the *time scale* and $\\lambda$ explained in the video?\n",
    "- What does the `x2` present?\n",
    "- What is the median value for this dataset (read from the statistics)? How much does it differ from the theoretical value (given in video)?\n",
    "- What is the [interquartile range](https://en.wikipedia.org/wiki/Interquartile_range) for this data?\n",
    "- How much do the theoretical probability $P(2 < x < 4)$ and the counted proportion values differ? Explain why.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.18690191 2.93789941 4.40606381 ... 5.04056397 3.15409525 3.763155  ]\n"
     ]
    }
   ],
   "source": [
    "# Create an array x2 of 2 000 random numbers having the parameter value lamda given in the Youtube video. This array simulates the real data.\n",
    "# scale = 1/lamda, lamda = 1/2, size = 2000\n",
    "from scipy.stats import expon\n",
    "import matplotlib.pyplot as plt\n",
    "sigma = 2\n",
    "size = 2000\n",
    "mean = 1.3863\n",
    "x2 = expon.rvs(loc=mean, scale=sigma, size=size, random_state=None)\n",
    "print(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median: 0.6931471805599453\n",
      "Mean: 1.0\n",
      "Standard deviation: 1.0\n",
      "Interquartile range : [0.28768207 0.69314718 1.38629436]\n"
     ]
    }
   ],
   "source": [
    "# calculate the descriptive statistics\n",
    "value = expon()\n",
    "print(\"Median:\", value.median())\n",
    "print(\"Mean:\", value.mean())\n",
    "print(\"Standard deviation:\", value.std())\n",
    "print(\"Interquartile range :\", value.ppf([0.25, 0.50, 0.75]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'The graph of exponentially distributed random numbers')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#Draw a histogram of the values\n",
    "plt.hist(x2, density=True , bins=30, edgecolor='black', rwidth=0.8)\n",
    "plt.ylabel('Probability')\n",
    "plt.xlabel('Data');\n",
    "plt.grid()\n",
    "plt.title('The graph of exponentially distributed random numbers')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'whiskers': [<matplotlib.lines.Line2D at 0x7fd1be9b6a30>,\n",
       "  <matplotlib.lines.Line2D at 0x7fd1be9b6dc0>],\n",
       " 'caps': [<matplotlib.lines.Line2D at 0x7fd1be9c6190>,\n",
       "  <matplotlib.lines.Line2D at 0x7fd1be9c6520>],\n",
       " 'boxes': [<matplotlib.lines.Line2D at 0x7fd1be9b66a0>],\n",
       " 'medians': [<matplotlib.lines.Line2D at 0x7fd1be9c68b0>],\n",
       " 'fliers': [<matplotlib.lines.Line2D at 0x7fd1be9c6c40>],\n",
       " 'means': []}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#Draw a boxplot data \n",
    "plt.boxplot(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(2 < x < 4) is 0.11701964434787848\n"
     ]
    }
   ],
   "source": [
    "#find the probability P(2 < x < 4)\n",
    "from scipy.stats import expon\n",
    "from matplotlib import pyplot\n",
    "# create distribution\n",
    "dist = expon()\n",
    "data = dist.cdf(4.0) - dist.cdf(2.0)\n",
    "print(\"P(2 < x < 4) is\", data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Amount of the values between 2 and 4: 938\n",
      "Proportion of the values between 2 and 4: 0.469\n"
     ]
    }
   ],
   "source": [
    "#Count the proportion of the values in the simulated data are between 2 and 4.\n",
    "a = ((2 <= x2) & (x2 <= 4)).sum()\n",
    "print(\"Amount of the values between 2 and 4:\", a)\n",
    "b = a / 2000\n",
    "print(\"Proportion of the values between 2 and 4:\", b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answers:**\n",
    "\n",
    "a) The value time scale is minutes and lamda is customer per minute in the video\n",
    "\n",
    "b) x2 is just a variable name\n",
    "\n",
    "c) The mean for this dataset is about 1. The difference between dataset and video is 1.3863 - 1 = 0.3863\n",
    "\n",
    "d) The Interquartile range : [0.28768207 0.69314718 1.38629436]\n",
    "\n",
    "e)The difference between theoretical probability and counted proportion values is 0.4735 - 0.117 = 0.3565. It has the diffence because probability when talking about the chances of some event happening in the future and proportion when describing some events actually happened in the past."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Problem 3\n",
    "\n",
    "In this problem we study how the accelerometer sensor measurements are distributed. Attached is an example data recorded with [Physics Toolbox Accelerometer](https://play.google.com/store/apps/details?id=com.chrystianvieyra.android.physicstoolboxaccelerometer) application that is freely available in Google Play. Make your own recording using this application:\n",
    "- Install the application to your mobile phone.\n",
    "- Open the application.\n",
    "- Place your mobile phone on the flat surface (for example on the table).\n",
    "- Click the (+) button to start recording.\n",
    "- Record at least 30 seconds of data.\n",
    "- Save the file and send it by email to yourself.\n",
    "\n",
    "Coding:\n",
    "- Open the file using Pandas read_csv function.\n",
    "   - You might need to define `sep` and `decimal` parameters for read_csv. See the documentation for details.\n",
    "- Create separate graphical plots of the accelerometer data (gFx, gFy, ...). Place the time on x-axis.\n",
    "- Calculate the descriptive statistics for the accelerometer data.\n",
    "- Create histograms and annotate the graphics with vertical lines at $\\mu \\pm \\sigma$.\n",
    "- Select randomly one row from the data and print out the values.\n",
    "\n",
    "Questions:\n",
    "- What are the mean values for gFx, gFy, and gFz? How can you predict the orientation of your mobile phone from these values?\n",
    "- Compare the standard deviations for gFx, gFy, and gFz. How much do they differ? Explain the similarities or diffences.\n",
    "- How does the histograms of the acceleration data look like? What probability distribution could fit to this data?\n",
    "- Study the randomly selected row from the data and compare it to the statistics. If you would get only one sample (like this), how confident you would be about the readings? Explain why.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>gFx</th>\n",
       "      <th>gFy</th>\n",
       "      <th>gFz</th>\n",
       "      <th>TgF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.006520</td>\n",
       "      <td>0.8431</td>\n",
       "      <td>0.0168</td>\n",
       "      <td>0.5685</td>\n",
       "      <td>1.017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.007143</td>\n",
       "      <td>0.8550</td>\n",
       "      <td>0.0181</td>\n",
       "      <td>0.5633</td>\n",
       "      <td>1.024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.007573</td>\n",
       "      <td>0.8416</td>\n",
       "      <td>0.0161</td>\n",
       "      <td>0.5674</td>\n",
       "      <td>1.015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.8578</td>\n",
       "      <td>0.0181</td>\n",
       "      <td>0.5689</td>\n",
       "      <td>1.029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.008318</td>\n",
       "      <td>0.8404</td>\n",
       "      <td>0.0195</td>\n",
       "      <td>0.5706</td>\n",
       "      <td>1.016</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       time     gFx     gFy     gFz    TgF\n",
       "0  0.006520  0.8431  0.0168  0.5685  1.017\n",
       "1  0.007143  0.8550  0.0181  0.5633  1.024\n",
       "2  0.007573  0.8416  0.0161  0.5674  1.015\n",
       "3  0.007954  0.8578  0.0181  0.5689  1.029\n",
       "4  0.008318  0.8404  0.0195  0.5706  1.016"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Open the file\n",
    "# define: decimal = ',' and sep = ';'\n",
    "import pandas\n",
    "file = pandas.read_csv('Android_data.csv')\n",
    "file.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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"
    }
   ],
   "source": [
    "#create a graph\n",
    "file.plot('time','gFx')\n",
    "file.plot('time','gFy')\n",
    "file.plot('time','gFz')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>gFx</th>\n",
       "      <th>gFy</th>\n",
       "      <th>gFz</th>\n",
       "      <th>TgF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>13397.000000</td>\n",
       "      <td>13397.000000</td>\n",
       "      <td>13397.000000</td>\n",
       "      <td>13397.000000</td>\n",
       "      <td>13397.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>17.011644</td>\n",
       "      <td>0.848517</td>\n",
       "      <td>0.014207</td>\n",
       "      <td>0.566123</td>\n",
       "      <td>1.020157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.830157</td>\n",
       "      <td>0.004242</td>\n",
       "      <td>0.004229</td>\n",
       "      <td>0.005094</td>\n",
       "      <td>0.004470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.006520</td>\n",
       "      <td>0.826900</td>\n",
       "      <td>-0.002400</td>\n",
       "      <td>0.511900</td>\n",
       "      <td>0.992000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>8.500180</td>\n",
       "      <td>0.845700</td>\n",
       "      <td>0.011400</td>\n",
       "      <td>0.562900</td>\n",
       "      <td>1.017000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>17.013007</td>\n",
       "      <td>0.848500</td>\n",
       "      <td>0.014600</td>\n",
       "      <td>0.566200</td>\n",
       "      <td>1.020000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>25.523445</td>\n",
       "      <td>0.851300</td>\n",
       "      <td>0.017000</td>\n",
       "      <td>0.569400</td>\n",
       "      <td>1.023000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>34.036185</td>\n",
       "      <td>0.872700</td>\n",
       "      <td>0.030200</td>\n",
       "      <td>0.597000</td>\n",
       "      <td>1.043000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               time           gFx           gFy           gFz           TgF\n",
       "count  13397.000000  13397.000000  13397.000000  13397.000000  13397.000000\n",
       "mean      17.011644      0.848517      0.014207      0.566123      1.020157\n",
       "std        9.830157      0.004242      0.004229      0.005094      0.004470\n",
       "min        0.006520      0.826900     -0.002400      0.511900      0.992000\n",
       "25%        8.500180      0.845700      0.011400      0.562900      1.017000\n",
       "50%       17.013007      0.848500      0.014600      0.566200      1.020000\n",
       "75%       25.523445      0.851300      0.017000      0.569400      1.023000\n",
       "max       34.036185      0.872700      0.030200      0.597000      1.043000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculate the descriptive statistics\n",
    "file.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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"
    }
   ],
   "source": [
    "#gFx \n",
    "std = np.std(file['gFx'])\n",
    "mean = np.mean(file['gFx'])\n",
    "s = np.random.normal(mean, std,400)\n",
    "plt.hist(file[['gFx']], density = True, bins = 4)\n",
    "plt.axvline(x=mean-1*std,linestyle='dashed', alpha=0.5,color='r')\n",
    "plt.axvline(x=mean+1*std,linestyle='dashed', alpha=0.5,color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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"
    }
   ],
   "source": [
    "#gFy\n",
    "std = np.std(file['gFy'])\n",
    "mean = np.mean(file['gFy'])\n",
    "s = np.random.normal(mean, std,400)\n",
    "plt.hist(file[['gFy']], density = True, bins = 4)\n",
    "plt.axvline(x=mean-1*std,linestyle='dashed', alpha=0.5,color='r')\n",
    "plt.axvline(x=mean+1*std,linestyle='dashed', alpha=0.5,color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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"
    }
   ],
   "source": [
    "#gFz\n",
    "std = np.std(file['gFz'])\n",
    "mean = np.mean(file['gFz'])\n",
    "s = np.random.normal(mean, std,400)\n",
    "plt.hist(file[['gFz']], density = True, bins = 4)\n",
    "plt.axvline(x=mean-1*std,linestyle='dashed', alpha=0.5,color='r')\n",
    "plt.axvline(x=mean+1*std,linestyle='dashed', alpha=0.5,color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "time    17.011644\n",
       "gFx      0.848517\n",
       "gFy      0.014207\n",
       "gFz      0.566123\n",
       "TgF      1.020157\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(file)\n",
    "df.sample()\n",
    "np.std(df)\n",
    "np.mean(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answers:**\n",
    "\n",
    "a)gFx, gFy, gFz represent for x, y, z asix, respectively. I think we can see the direcion and the orientation of the device from mean values.\n",
    "\n",
    "b)From file.describe(), the standard deviation is 0.004242\t0.004229\t0.005094 for gFx, gFy, and gFz. The gFx, and gFy are almost the same and close to gFz value, so it does not have much differences\n",
    "\n",
    "c)Histograms are look like ripples of model and normal distribution can fit this data\n",
    "\n",
    "d)I can see the data from randomly selected row matches to statistics, so i can say the values are the same for all values after prediction so I would confidently get any sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}