{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "##set color scheme\n",
    "light_green=\"#36B37E\"\n",
    "mid_green=\"#00875A\"\n",
    "dark_green=\"#006644\"\n",
    "\n",
    "light_red=\"#DCBCBC\"\n",
    "mid_red=\"#B97C7C\"\n",
    "dark_red=\"#8F2727\"\n",
    "\n",
    "ink=\"#172B4D\"\n",
    "light_highlight=\"#505F79\"\n",
    "fade = \"#B3BAC5\"\n",
    "dark_fade=\"#8993A4\"\n",
    "\n",
    "import numpy as np\n",
    "import scipy.special\n",
    "import scipy.stats as st\n",
    "import scipy.optimize as opt\n",
    "from scipy.stats import beta\n",
    "\n",
    "from math import sqrt as sqrt\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "plt.style.use('seaborn-white')\n",
    "\n",
    "import pandas as pd \n",
    "import altair as alt "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame({\n",
    "    'Country': ['Africa', 'Asia', 'Europe', 'Middle East', 'North America'],\n",
    "    'number_students': [1, 16, 10, 1, 5]}\n",
    ")\n",
    "\n",
    "num_students = alt.Chart().mark_bar().encode(\n",
    "        y='Country',\n",
    "        x=alt.X('number_students', title='Number of students', scale=alt.Scale(domain=(0, 16)))\n",
    ")\n",
    "\n",
    "chart = alt.layer(num_students).properties(\n",
    "    data=data\n",
    ").configure_view(\n",
    "        height=400,\n",
    "        width=500\n",
    ").configure_axis(\n",
    "        titleFontSize=14,\n",
    "        titleFontWeight='normal'\n",
    ").properties(\n",
    "    width=600,\n",
    "    height=175\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v2+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v2.4.3.json",
       "config": {
        "axis": {
         "titleFontSize": 14,
         "titleFontWeight": "normal"
        },
        "axisX": {
         "labelFontSize": 14
        },
        "axisY": {
         "labelFontSize": 14
        },
        "scale": {
         "bandPaddingInner": 0.3,
         "bandPaddingOuter": 1
        },
        "view": {
         "height": 400,
         "width": 500
        }
       },
       "data": {
        "values": [
         {
          "Country": "Africa",
          "number_students": 1
         },
         {
          "Country": "Asia",
          "number_students": 16
         },
         {
          "Country": "Europe",
          "number_students": 10
         },
         {
          "Country": "Middle East",
          "number_students": 1
         },
         {
          "Country": "North America",
          "number_students": 5
         }
        ]
       },
       "height": 175,
       "layer": [
        {
         "encoding": {
          "x": {
           "field": "number_students",
           "scale": {
            "domain": [
             0,
             16
            ]
           },
           "title": "Number of students",
           "type": "quantitative"
          },
          "y": {
           "field": "Country",
           "type": "nominal"
          }
         },
         "mark": "bar"
        }
       ],
       "width": 600
      },
      "image/png": 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",
      "text/plain": [
       "<VegaLite 2 object>\n",
       "\n",
       "If you see this message, it means the renderer has not been properly enabled\n",
       "for the frontend that you are using. For more information, see\n",
       "https://altair-viz.github.io/user_guide/troubleshooting.html\n"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chart.configure_scale(\n",
    "        bandPaddingInner=0.3,\n",
    "        bandPaddingOuter=1\n",
    ").configure_axisX(labelFontSize=14\n",
    ").configure_axisY(labelFontSize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame({\n",
    "    'Background': ['Technical', 'Non-Technical'],\n",
    "    'number_students': [15, 16]}\n",
    ")\n",
    "\n",
    "num_students = alt.Chart().mark_bar().encode(\n",
    "        y='Background',\n",
    "        x=alt.X('number_students', title='Number of students', scale=alt.Scale(domain=(0, 16)))\n",
    ")\n",
    "\n",
    "chart = alt.layer(num_students).properties(\n",
    "    data=data\n",
    ").configure_view(\n",
    "        height=400,\n",
    "        width=500\n",
    ").configure_axis(\n",
    "        titleFontSize=14,\n",
    "        titleFontWeight='normal'\n",
    ").properties(\n",
    "    width=600,\n",
    "    height=175\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v2+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v2.4.3.json",
       "config": {
        "axis": {
         "titleFontSize": 14,
         "titleFontWeight": "normal"
        },
        "axisX": {
         "labelFontSize": 14
        },
        "axisY": {
         "labelFontSize": 14
        },
        "scale": {
         "bandPaddingInner": 0.3,
         "bandPaddingOuter": 1
        },
        "view": {
         "height": 400,
         "width": 500
        }
       },
       "data": {
        "values": [
         {
          "Background": "Technical",
          "number_students": 15
         },
         {
          "Background": "Non-Technical",
          "number_students": 16
         }
        ]
       },
       "height": 175,
       "layer": [
        {
         "encoding": {
          "x": {
           "field": "number_students",
           "scale": {
            "domain": [
             0,
             16
            ]
           },
           "title": "Number of students",
           "type": "quantitative"
          },
          "y": {
           "field": "Background",
           "type": "nominal"
          }
         },
         "mark": "bar"
        }
       ],
       "width": 600
      },
      "image/png": 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Wl9FkdRlNVpfRZHUZTVaX0WR19TVgnw18iHI+7HOBiyhHsXP2EHnm5uZ6+w2rz/T5m19fMZrA6TKawOkymsDpMprA6TKawOkymsDpMprA6erLtJ9yFpGdfdxZMlwyYHeP0QROl9EETpfRBE6X0QROl9EETpfRBE6X0QROV59HsOeBe4CTgK2UV3Gsm0iTAbt7jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuvoyncPCtdftHidPctQmA3b3GE3gdBlN4HQZTeB0GU3gdBlN4HQZTeB0GU3gdPVl2gXcBuyb0i9RXkY9ESYDdvcYTeB0GU3gdBlN4HQZTeB0GU3gdBlN4HQZTeB0GU3JgMmA3T1GEzhdRhM4XUYTOF1GEzhdRhM4XUYTOF1GEzhdfZkuYOklIvUykR8DO/p4sKS/ZMDuHqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnK6+TGfSnPf6bmAvcIBmuP5R9fZzLH61x2TEZMDuHqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnK6+TB8BjgKnTVz+0eryrcB55FUddcmA3T1GEzhdRhM4XUYTOF1GEzhdRhM4XUYTOF1GEzhdfZnuAP7A4heWOQE4AlwIbAJeA97fxwMm/SQDdvcYTeB0GU3gdBlN4HQZTeB0GU3gdBlN4HQZTeB09WW6nrIE5KqJy2+iOWp9BTmCrUsG7O4xmsDpMprA6TKawOkymsDpMprA6TKawOkymsDp6su0hXIEu15z/TRlmJ4HHgDeV739NFmDrUoG7O4xmsDpMprA6TKawOkymsDpMprA6TKawOkymsDp6tM0A9wA/JYySB+q3p8BTqY88XFrXw+W9JMM2N1jNIHTZTSB02U0gdNlNIHTZTSB02U0gdNlNIHT1ZfpfOBDUy7fRTlzSJaFSDM3Nzd/8/2HH7L1X555Secymqwuo8nqMpqsLqPJ6jKarC6jyeoymm6+//C1G3nAvpiyBOSC1mX7aE7dlwFbmjJg/1uapmmapuk67OGHNvKAfSLwJ8owfR1wmDJcv0A5PV8iTQbsNE3TNE3Xbzf2gA3NkD1f9aa+7jhZu2TATtM0TdN0/XZjDtinA++o/j0VOJdyFPsosJuyNOR0Fp8fO5EkA3aapmmapuu3G2/A3kFztHqlnvqmpcmaJAN2mqZpmqbrtxtvwN4C7AEuWaEfoLyiYyJMBuw0TdM0TddvN96APZmLgcdpziRyN/BNcu5rdTJgp2mapmm6fruxB+wLaJaD7Kkue4Dm1Rs39/EgSf/JgJ2maZqm6frtxh6w7wBep6zLbueDlCH7wj4eJOk/GbDTNE3TNF2/3dgD9m3Aa8Cmics3VZdf2ceDrEF2A1cDVy3RS1Z5v9spLxO/2hfY2QN8eJW3bWc3cNlyH5ABO03TNE3T9duNPWDfAhwHrpm4/GbKEWzri83sZ/mzn7zG6pa3XFTdfjW/WMxQXqDn9VU+djt3sMLnkAE7TdM0TdP12409YG8B/kAZKo8Dz1POhz0PPMbiI9uWbKUsa9lGOWI8D3yc8qI59eWrSb0m/dJV3n4WeOcqb9vObcCLLLP9M2CnaZqmabp+u7EHbChHXm8Afkt5YuMTwCdZPy8yUw/Fl09cfjNwhPKLw6+AXa3rZoGDNL9YfJVytLi+r/uAp2ie7HladbuPAg9SlqH8pbr+IcovKgBfAr5Bs+1uovmF5WnKEXKq6/cBL1fXPQ/8XcuXATtN0zRN0w3cjT9gQzny2+4O4DmaM4uYM23A/lp12S+A2ylD7hHgbZTP7dXqsr2UAXke+CILz6ryCHBX9fZhylB8W+v6e4GHq7fvqh73EPASZVjfW113gGbYPwKcBFxfXfcw8BmaYb5+UmkG7DRN0zRNN3A39oB9IuWI9VJrmVe7VGLITA7Yu6r3b299zLuqyz4L3Fi93X4y4tPA71v3dVfrujtoBuNbq+uvqq6bAZ6lLKeZoRwVf46yhOUVymBeD8n1+u49wOeBR1uPccbE55ABO03TNE3TDdyNPWBfQzNQHqYsWdhHGShfZX0sE5kcsOtB9gXg28APgF/SHHW+k/JExC2t+9hM+WVj2hrsWylHu2dbb+9sXV8P1Ztbb59C2YafnLBub719GXAPZWlO/QvN1AH7wIEDP5+bm5uf7Pj/OdI0TdM0TVfTjT1g30F5kiOUwfr31du7KWuT393Hg6xxJgfs+v1XgJ9R1l8/SFlX/bfAHGUInnZ0eNpyk2kDdvs0fvVQvan19jlT7qedh6rr/wz8kLLtcwQ7TdM0TdO3SN86A/b7aI7s1ufBvqKPB1njLDVgt4fbTZRh+xyWPgr9xBK3Xc2AfRJl+93T+rjdNEfHX6McTZ92HWTATtM0TdN0Q3djD9hXUAa77wLnV2/vo5wHerkjsKZMDsWbKMPpUcoLzpxFWe88Txmwd9OchvBMmqPHX5xyX7DygP04zRKR9ttzlL8CXAu8l3KmkPqJln+hPLHxLMpQ/Wr1uJ+r7jMDdpqmaZqmG7gbe8CeoaxTro/o1oPoPM0waM9uFj9p8UzKEpH2Ezavbl1/3cR1c5Q12PV9tddg76UM6ydTniB5lIVHv+donszYfns75awi9WMcAz5S3eamice/jzJQHwdOpQzySy1jKQ+aATtN0zRN03XbjT1g12k/4e9SypHtrX0+wEg5i/LCL1umXLedMsyessaG2epxJp8wejLl7Cb1i+JsppxCsFMyYKdpmqZpun67cQfscylnEdldvf8pyllEXgW+yZt/ue9kDZMBO03TNE3T9duNOWDfycIlCk9W//5PmlcofOBNGpM1TAbsNE3TNE3XbzfegL2NcpT6T5Sj2PfQvJR3vZTiPhY/mS8RJQN2mqZpmqbrtxtvwN5BeQJjfaaMEyinjfuH1secQwZsdTJgp2mapmm6frvxBuxtLBywoRy9bp/z+gIyYKuTATtN0zRN0/XbjTtgt09Fdxj4UOv93WTAVicDdpqmaZqm67cbc8B+DfgF5cwhn6GcM/q+6v1PA3eTAVudDNhpmqZpmq7fbrwBu16DPb9CM2CLkwE7TdM0TdP12403YAOcDryD8gIoS/V0Fr84SiJJBuw0TdM0TddvN+aAnazzZMBO0zRN03T9NgN2IkwG7DRN0zRN128zYCfCVAP2i7Z+/9F/17mMJqvLaLK6jCary2iyuowmq8tosrqMphvvP7zfOMwaTcmAmZubU34DGL8xjSZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoymZMBkwO4eowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpGTAZsLvHaAKny2gCp8toAqfLaAKny2gCp8toAqfLaAKny2hKBkwG7O4xmsDpMprA6TKawOkymsDpMprA6TKawOkymsDpMpqSAZMBu3uMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKZkwGTA7h6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoykZMBmwu8doAqfLaAKny2gCp8toAqfLaAKny2gCp8toAqfLaEoGTAbs7jGawOkymsDpMprA6TKawOkymsDpMprA6TKawOkympIBkwG7e4wmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpmTAZMDuHqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKRkwGbC7x2gCp8toAqfLaAKny2gCp8toAqfLaAKny2gCp8toSgZMBuzuMZrA6TKawOkymsDpMprA6TKawOkymsDpMprA6TKakgGTAbt7jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoymZMBkwO4eowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpGTAZsLvHaAKny2gCp8toAqfLaAKny2gCp8toAqfLaAKny2hKBkwG7O4xmsDpMprA6TKawOkymsDpMprA6TKawOkymsDpMpqSAZMBu3uMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKZkwGTA7h6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoykZMBmwu8doAqfLaAKny2gCp8toAqfLaAKny2gCp8toAqfLaEoGTAbs7jGawOkymsDpMprA6TKawOkymsDpMprA6TKawOkympIBkwG7e4wmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpmTAZMDuHqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKRkwGbC7x2gCp8toAqfLaAKny2gCp8toAqfLaAKny2gCp8toSgZMBuzuMZrA6TKawOkymsDpMprA6TKawOkymsDpMprA6TKakgGTAbt7jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoymZMBkwO4eowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpGTAZsLvHaAKny2gCp8toAqfLaAKny2gCp8toAqfLaAKny2hKBkwG7O4xmsDpMprA6TKawOkymsDpMprA6TKawOkymsDpMpqSAZMBu3uMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKZkwGTA7h6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoykZMBmwu8doAqfLaAKny2gCp8toAqfLaAKny2gCp8toAqfLaEoGTAbs7jGawOkymsDpMprA6TKawOkymsDpMprA6TKawOkympIBkwG7e4wmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpmTAZMDuHqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKRkwGbC7x2gCp8toAqfLaAKny2gCp8toAqfLaAKny2gCp8toSgZMBuzuMZrA6TKawOkymsDpMprA6TKawOkymsDpMprA6TKakgGTAbt7jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoymZMBkwO4eowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpGTAZsLvHaAKny2gCp8toAqfLaAKny2gCp8toAqfLaAKny2hKBkwG7O4xmsDpMprA6TKawOkymsDpMprA6TKawOkymsDpMpqSAZMBu3uMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKZkwGTA7h6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoykZMBmwu8doAqfLaAKny2gCp8toAqfLaAKny2gCp8toAqfLaEoGTAbs7jGawOkymsDpMprA6TKawOkymsDpMprA6TKawOkympIBkwG7e4wmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpmTAZMDuHqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKRkwGbC7x2gCp8toAqfLaAKny2gCp8toAqfLaAKny2gCp8toSgbMwYMH/+/c3Nx8mqapvdlfpWm6Xnro0KH/M/aMl4yYuTnnEWyjy2gCp8toAqfLaAKny2gCp8toAqfLaAKny2gCp8toSgaM9RvA6DKawOkymsDpMprA6TKawOkymsDpMprA6TKawOkympIBY/0GMLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jKZkwFi/AYwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuowmcLqMpGTAHDhz4+diGaTG6jCZwuowmcLqMJnC6jCZwuowmcLqMJnC6jCZwuoymJEmSJEmSJEmSJEmSJEmSJEmShdkOnA5sGxsC7BwbMJFdwLuAU8eGtLIdeCcwOzZkiczi+F4yp/4avmNsyDrILGVb7Rgb0spWiumUsSHAZuBtS1w35r59OddWfKYx9/XbgS1LXD7Wvn65bVVnjH39UttqrbPUbLKZ8n/sdGBmOE5izwzwA2C+1etG9LwfOI5jcJwB/omF2+YA5T/3mLmOhaaXKTYcJygAAAyhSURBVD8ULDmf4vrB2BDg71m4reaB54BNY6KAL7DQ9CTj/kJyB4u3U93LR3RtBx6d8NzN+F+/q1hoeopxh/+vAq9SftDXMezbp7mg2F4AfjSwB5beVmPu63cAx4ArJi4fe1+/1Nevzhj7+qW21Vrv65eaTS4BjrQe8whwdk+Pmazz3ED5pvg+cCbwm+r98wZ2nA3cBLxG+c9jGLC/QdkW/wicAeyv3v/6iKbdleEQcC7wCcp/6MOMP3RAGRJfoRjvGdkCZTs9A9wM7Ks65i+QABdTts8jlCNm+6r3bx/RdAnwlcpwZ2V6tXLtGdG1vzLcRNlHPFi9f+mIprNphuoLgU9S9lmPjGDZQxmC5oGnWbgPGHPfvpRrK+UXtp8z/D5iuW011r5+FrgW+FcW/zK7m/H29cttqzpD7+uX21awdvv65WaTHdXlL1P+X11WfcwT5Ej2Wz5bgBeBx2i+GXZS/hN/e2DLYZrfAA0D9gxlx3Jw4vKnGPcI6OdZ/Fv0fuAllj7KMGTqH5zzwF0jW2aA/6D8YDLlIOXr1f4euhvYOw5namYp+4GvjGiYofx/O9y6rD569cVRRCV/Xxl2TrlsyP3WNhYeOWsPQmPu25dzXdS6fMgBeznTmPv6yb8ctYfGsfb1y22rdobe1y+3rdZyX7/cbHLLlMuuAX6M44BXMmLq374md3IHKTuWMQa2O3EM2AD/ifKfpc4myg+tsbYNlO3yAZofmruA51l6JzhkrqHshC6jHNkY+wj2Nsr39/8AfkFZanAD4x5ZqAefHwLXA78EvkP5OlpSD7YvMc46x3bupflz8NtojiyOeQT7VsoAclLrsvoH7WkDWzbRfL3aw+DY+/alXPV19bA/5D5iOdPY+/oPsHhoHHNfv9y2gnH39dO21RD7+mmzyU+APwEfBX4K/IyylCRJ/v835ecmLq93wmMMbLfiGbDbOZlmLejNI1tg8VGGG8flsKty/APlB9K0H+5D51002+cx4C80ayvHGrJ30Cy9mKf8SbN++7KRTJO5nuL54NgQytKGyXWVrzPu4H8LC7fPFuC31WVXjmSa3Gdb9u1LPV7tG2MfsdI2GGNffwFLP99hzH39tG019r5+2rYaYl8/bTZ5pPW4L1TXzzPuX/4SSeqd3OQPhTGPYNsG7BmaNbLzlCenGTJD+brVv1UfpfxgGCNbgD/QrA0c84dnO2cCD1HWMtb5FuXreOEIHmi2zVGaJyvtogzdhidfbqH8cHpSYJmhDK7HKd/nF1OOEM0DXx7R1V57+gzND9UxjmDXWWrAHnvfvp4G7DH39csN2GPu6ye3lWFfP21bDbGvnzabPF49xtXV+/Uv25NLyJK3YKb9GXGG8mSBB0YRuQbsEyk7k/o34bF+eLZzAfDhics+xLhne6iftDdPebLHsdb7hkGtnd2Mu62W+tP9IcZdelSn/vPrWEdi26m31b2ty2aAZxn/Sb0zlCeE/gy4Dfga4+63Jgchy759vQzYY+/rpw2Nhn395LYy7OuX+2Wknd0dP65rps0m9X570wofl7wFU68zO0TzDTLG2rh2TN+cP6VYLhkb0sohFv+J/G8Yd2icpTzj/HbKnw3vofmT2ecYbznGXsq22tq67GOMu/yh/X+uHcuAfTeL1xePFesvI1cAvwdOaF32IOMuXZkchCz79vUyYI+9r582NBr29ZPbyrCvn7athtjXT5tNfsLi/eUYT3hOpLmV8k34n4H3Uv5THwPePaLH8M25jfJn+2OUNZe3t/qZEV31k0t+SvkaXUn5QWUZiqAMHq8y/llE6m11L2VbXUHZTmM/ea/+P3cXZXnIV6r3941ogmYoG+N0c9NSPyH0GPBpyottfJnxl4hcQrPPPJVmWcFnRzQ9zvQjaWPv26e5YNwBe9Jk2NdPGxoN+/qlvn51xtjXL7et1nJfP202qS2PAWcBH6/eP0hO05cw/QT7Vy97i7XNtNPejJF6pzv5BKt5xl0rO+3FI45STn9lSb1Gdf/IDig7/va2eoEyqI2ZGZojP3W/x/g75B2UH0pjno97MmcCf2bhtnqY8Y/0T3797mfcJStzLD67hGHfPs0Fzf51jF/CJ02Gff3u6vHaS0IM+/qlvn51xtjX72bxtoK139cvNZvUTwqv+xSuV5xNBDmTcpTj7WNDkk6ZpXy9zhobsg6ynbKdxh6sJ3MyxZT/cyvndMr3+xgvYb1U6pdvN5mmJfv29Z3s67tnrH391uoxTx/4cZMkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSdYyZwPXUc5zPJnLgAvX4DF3Ajew8CWJh85OyssRf4FhX5xnC+WV/cZ+EawkSZIkSZJkjXIH5ZXDpr0c8J+AH63BY14MHGfcIfMQ5fM+zBt7lb0zKa9Kd/4qH3cH5ZXcrlzl7fu0JEmSJEmSJGuQW2lennfy5c0PUV7Ou+9cQBkyt6/BfXfN7ygvIf1Gs5uyrf5mlY97AvAacPkqb9+nJUmSJEmSJFmDtAfsY8AZrevaA/bXgO/TLKc4kTKkXkw58v3PwFeB+6v7egI4D/hh9f4r1cdCGbCPU46ev1hdPwec0nrsXcDB6rrnKUtK6lwL/Bi4EzjK9CPhs9V9zleP9T2aJSl3VZ/rceC7LF4iMgN8ufqYeeBJyksYnwG82tpWF6+wXai2zXeqj38euBE4QjNgt68/Bnyj5TwDeKz62Keqx316GcvJwM9ovp4/qTxJkiRJkiTJgLmVMvBdUv17iGZYbA/Yh4DngM3V+ztoBsUdlKOy88Cz1W3qIe8oZWh8rXr7ZMqAXV//U+BbLFymMlvd9zHgNuBRFh5h39u6/RPA2yY+p22U4fNY9bFfqz72EGU5yJeq+3+lus/JAfuG6uO/Bdxc2Y9QlmTUg+4zlCPIy20XgEdan+cDLffl1eM+W73/zdZ2eKy67qLWxz/W2q6Hq200afmvrW12Z3XdQZIkSZIkSZJBcyvNco19lKHs76rr2gP2QcogWa9X3kYzSG6jDKFP0gyac5SB+rTq/Y9VjzNLM2DvazmurS67FLi3uu+TWtf/FHidMoDX5qXWHtcD8rmtyz5VXbanev93wNeXuP1c9VgnVO+/kzLgvp1mWcb7q+uW2y5nVx97Z+u+678YXE7ZJm0TwPXVZe+m2U7tZTr7abZN21L/UvFw62OvoRzRfiNrzJMkSZIkSZI3mXpYnaUMYi9SBritwG95YwP2XRP3+2Lr489n4YBdv13nDJrB8/Hq7R9Tlph8m+aI9izlCG37viezv/K0n7R5Xuv+Yfn15fWQWx8B/gTNsF0PvfX9LLdd2r9U1NlZXXZ59XnMA78G7qMsFXmmuuzK1mNd2rp9++s1aXmIZsnIgxO3S5IkSZIkSQZKe2CDZmj7DvDfWH7Arp+sV7/dHlgnh+D2UF2/vbP18btohsV67fUc8Kuq36nuf9uU+57M3IQVyoDfdcCuP/4BmnXYxyhLRLoM2PV2mdy2k59nfTT7X4FfVp/njyhH8N815bFg+QEb4GrKwF7/gvAnFp8dJkmSJEmSJFnDTBsCv0szoNVHpR+nDJL1euV6ffBqB+x54MOtj7+kuuyDlOH3JRYOyB+jLOmYmXLf0z6noyw8S8lHWLgcY7kB+27KucHrXMzSR5WX2y4XsfgI9PtZOGAfY+GTO99JORK9g+4D9qWUJzP+irIspc5eFn9tkyRJkiRJkjXOtAG7Xs/bXv+7v3r/05Sju/WTGi+jeZLjGx2wjwEfoAydr9E8yfGq6vr7qo//RPX+I0vc92Tqo9WPUY4676Es22g/GXG5AbteP34J5Sj7LdX9XUizrvofKeugV9our9KcQWVP6/rLaY5mPwOcBbyv+vjXKV+DlQbstuXk6rbPVJ/zqcA/sXgte5IkSZIkSbLG2Utzdo92rmDhEezTKINi+6wW7SPYr7B4DXZ76UR7wK4H4Odb93eEsiyizp2t6+YpZ8zYtsR9T8unJ27/MnB66/pDwH9Z4rbvphmE695XPd4WmlMLfmyF7dL+vOvr6/XlH6yu//DE9UdpjkLvZvER8Ftovl6TlmsnzPOU0wImSZIkSZIk0mymDKmnrPSBbyCz1X1Oe7nynZShe7WPtx14DwsH967ZTDmq/F7K2UMmc+LExy63XbZWhlNXuP4dq3BOWrZX9/Veml9IkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkmTZ/D+nteGgZvakZAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<VegaLite 2 object>\n",
       "\n",
       "If you see this message, it means the renderer has not been properly enabled\n",
       "for the frontend that you are using. For more information, see\n",
       "https://altair-viz.github.io/user_guide/troubleshooting.html\n"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chart.configure_scale(\n",
    "        bandPaddingInner=0.3,\n",
    "        bandPaddingOuter=1\n",
    ").configure_axisX(labelFontSize=14\n",
    ").configure_axisY(labelFontSize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_function(x):\n",
    "    return 5*(x-5)**2 + 3*(x-5)**3+5\n",
    "\n",
    "# generate grid for plotting\n",
    "x = np.linspace(0, 10, 400, endpoint=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1760x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(11, 4), dpi=160)\n",
    "\n",
    "# limits\n",
    "plt.xlim(3.0, 6.0)\n",
    "plt.ylim(0.0, 10.0)\n",
    "\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.spines['left'].set_color(light_highlight)\n",
    "ax.spines['bottom'].set_color(light_highlight)\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "plt.xlabel('$x$ or independent variable', fontsize=18)\n",
    "plt.ylabel('$y$ or dependant variable', fontsize=18)\n",
    "\n",
    "plt.plot(x, simple_function(x), color=dark_red, linewidth=2.0, linestyle=\"-\")\n",
    "plt.title(\"\")\n",
    "plt.savefig(\"graph1.png\", dpi=160)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1760x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def exercise_function1(x):\n",
    "    return -100000 + 28000*x\n",
    "\n",
    "# generate grid for plotting\n",
    "x = np.linspace(-10, 10, 400, endpoint=True)\n",
    "plt.figure(figsize=(11, 4), dpi=160)\n",
    "\n",
    "# limits\n",
    "plt.xlim(0.0, 6.0)\n",
    "plt.ylim(-120000.0, 120000.0)\n",
    "\n",
    "\n",
    "plt.plot(x, exercise_function1(x), color=dark_red, linewidth=2.0, linestyle=\"-\")\n",
    "plt.savefig(\"graph2.png\", dpi=160)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1760x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fixed_point(x):\n",
    "    return x\n",
    "\n",
    "# generate grid for plotting\n",
    "x = np.linspace(0, 10, 400, endpoint=True)\n",
    "plt.figure(figsize=(11, 4), dpi=160)\n",
    "\n",
    "\n",
    "# limits\n",
    "plt.xlim(0.0, 5.0)\n",
    "plt.ylim(0.0, 5.0)\n",
    "\n",
    "plt.plot(x, fixed_point(x), color=light_red, linewidth=2.0, linestyle=\"-\", label=\"$f(x) = x$\")\n",
    "plt.plot(x, x**2, color=dark_red, linewidth=2.0, linestyle=\"-\", label=\"$f(x) = x^2$\")\n",
    "plt.plot(x, x**(1/2), color=ink, linewidth=2.0, linestyle=\"-\", label=\"$f(x) = \\sqrt{x}$\")\n",
    "plt.legend(loc='upper left', fontsize=10)\n",
    "plt.savefig(\"graph3.png\", dpi=160)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fixed_point(x):\n",
    "    return 3*x**2 - 3*x - 4\n",
    "\n",
    "# generate grid for plotting\n",
    "x = np.linspace(-10, 10, 400, endpoint=True)\n",
    "plt.figure(figsize=(6, 4), dpi=160)\n",
    "\n",
    "## axes \n",
    "ax = plt.gca()\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.spines['left'].set_color(light_highlight)\n",
    "ax.spines['bottom'].set_color(light_highlight)\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# limits\n",
    "plt.xlim(-5.0, 5.0)\n",
    "plt.ylim(-10.0, 35.0)\n",
    "\n",
    "plt.plot(x, fixed_point(x), color=dark_red, linewidth=2.0, linestyle=\"-\", label=\"$f(x) = 3x^2 - 3x - 4$\")\n",
    "\n",
    "plt.legend(loc='upper center', fontsize=10)\n",
    "plt.title(\"$a > 0$, curve has a minimum\", loc='left', pad=10, color=lines, fontsize=10)\n",
    "\n",
    "plt.savefig(\"graph4.png\", dpi=160)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fixed_point(x):\n",
    "    return -x**2 + 4*x - 2\n",
    "\n",
    "# generate grid for plotting\n",
    "x = np.linspace(-10, 10, 400, endpoint=True)\n",
    "plt.figure(figsize=(6, 4), dpi=160)\n",
    "\n",
    "## axes \n",
    "ax = plt.gca()\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.spines['left'].set_color(light_highlight)\n",
    "ax.spines['bottom'].set_color(light_highlight)\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# limits\n",
    "plt.xlim(-1.0, 5.0)\n",
    "plt.ylim(-3.0, 3.0)\n",
    "\n",
    "plt.plot(x, fixed_point(x), color=dark_red, linewidth=2.0, linestyle=\"-\", label=\"$f(x) = -x^2 + 4x - 2$\")\n",
    "\n",
    "plt.legend(loc='upper center', fontsize=10)\n",
    "plt.title(\"$a < 0$, curve has a maximum\", loc='left', pad=10, color=lines, fontsize=10)\n",
    "\n",
    "plt.savefig(\"graph5.png\", dpi=160)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}