From 78cae18ebb66af2c91e565487617c11e74601c68 Mon Sep 17 00:00:00 2001
From: Siqi Wang <siqiwang@hawaii.edu>
Date: Thu, 29 Aug 2024 17:44:26 +1000
Subject: [PATCH] added solution for Extended exercise

---
 notebooks/Module 1.1.2 - Distributions.ipynb | 283 ++++++++-----------
 1 file changed, 119 insertions(+), 164 deletions(-)

diff --git a/notebooks/Module 1.1.2 - Distributions.ipynb b/notebooks/Module 1.1.2 - Distributions.ipynb
index 4063f17..ac2a241 100644
--- a/notebooks/Module 1.1.2 - Distributions.ipynb	
+++ b/notebooks/Module 1.1.2 - Distributions.ipynb	
@@ -40,7 +40,7 @@
     {
      "data": {
       "text/plain": [
-       "6"
+       "3"
       ]
      },
      "execution_count": 1,
@@ -82,7 +82,7 @@
     {
      "data": {
       "text/plain": [
-       "Counter({1: 16752, 6: 16755, 2: 16819, 5: 16444, 3: 16653, 4: 16577})"
+       "Counter({4: 16749, 5: 16733, 2: 16724, 1: 16663, 3: 16574, 6: 16557})"
       ]
      },
      "execution_count": 3,
@@ -127,12 +127,12 @@
      "output_type": "stream",
      "text": [
       "   state  count\n",
-      "0      1  16752\n",
-      "1      2  16819\n",
-      "2      3  16653\n",
-      "3      4  16577\n",
-      "4      5  16444\n",
-      "5      6  16755\n"
+      "0      1  16663\n",
+      "1      2  16724\n",
+      "2      3  16574\n",
+      "3      4  16749\n",
+      "4      5  16733\n",
+      "5      6  16557\n"
      ]
     },
     {
@@ -140,28 +140,28 @@
       "text/html": [
        "\n",
        "<style>\n",
-       "  #altair-viz-d106aa678e3e49cebe1663351ad662be.vega-embed {\n",
+       "  #altair-viz-227f8e1cf33a460bb96b338f76ee1adf.vega-embed {\n",
        "    width: 100%;\n",
        "    display: flex;\n",
        "  }\n",
        "\n",
-       "  #altair-viz-d106aa678e3e49cebe1663351ad662be.vega-embed details,\n",
-       "  #altair-viz-d106aa678e3e49cebe1663351ad662be.vega-embed details summary {\n",
+       "  #altair-viz-227f8e1cf33a460bb96b338f76ee1adf.vega-embed details,\n",
+       "  #altair-viz-227f8e1cf33a460bb96b338f76ee1adf.vega-embed details summary {\n",
        "    position: relative;\n",
        "  }\n",
        "</style>\n",
-       "<div id=\"altair-viz-d106aa678e3e49cebe1663351ad662be\"></div>\n",
+       "<div id=\"altair-viz-227f8e1cf33a460bb96b338f76ee1adf\"></div>\n",
        "<script type=\"text/javascript\">\n",
        "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
        "  (function(spec, embedOpt){\n",
        "    let outputDiv = document.currentScript.previousElementSibling;\n",
-       "    if (outputDiv.id !== \"altair-viz-d106aa678e3e49cebe1663351ad662be\") {\n",
-       "      outputDiv = document.getElementById(\"altair-viz-d106aa678e3e49cebe1663351ad662be\");\n",
+       "    if (outputDiv.id !== \"altair-viz-227f8e1cf33a460bb96b338f76ee1adf\") {\n",
+       "      outputDiv = document.getElementById(\"altair-viz-227f8e1cf33a460bb96b338f76ee1adf\");\n",
        "    }\n",
        "    const paths = {\n",
        "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
        "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
-       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
+       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.17.0?noext\",\n",
        "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
        "    };\n",
        "\n",
@@ -197,12 +197,12 @@
        "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
        "    } else {\n",
        "      maybeLoadScript(\"vega\", \"5\")\n",
-       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
+       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.17.0\"))\n",
        "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
        "        .catch(showError)\n",
        "        .then(() => displayChart(vegaEmbed));\n",
        "    }\n",
-       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"name\": \"data-6c014555b2ed00ff58bfff3019c115a1\"}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"field\": \"state\", \"type\": \"ordinal\"}, \"y\": {\"field\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\", \"datasets\": {\"data-6c014555b2ed00ff58bfff3019c115a1\": [{\"state\": 1, \"count\": 16752}, {\"state\": 2, \"count\": 16819}, {\"state\": 3, \"count\": 16653}, {\"state\": 4, \"count\": 16577}, {\"state\": 5, \"count\": 16444}, {\"state\": 6, \"count\": 16755}]}}, {\"mode\": \"vega-lite\"});\n",
+       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"name\": \"data-5e063898c6115c8b45f052fe01116679\"}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"field\": \"state\", \"type\": \"ordinal\"}, \"y\": {\"field\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.17.0.json\", \"datasets\": {\"data-5e063898c6115c8b45f052fe01116679\": [{\"state\": 1, \"count\": 16663}, {\"state\": 2, \"count\": 16724}, {\"state\": 3, \"count\": 16574}, {\"state\": 4, \"count\": 16749}, {\"state\": 5, \"count\": 16733}, {\"state\": 6, \"count\": 16557}]}}, {\"mode\": \"vega-lite\"});\n",
        "</script>"
       ],
       "text/plain": [
@@ -259,7 +259,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -302,7 +302,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -324,12 +324,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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i3nnnHSxZsgQAIJfLcfToUWzZsgXNzc2Ii4vDggUL8MILL3Dah8jNfXOmHqIITIwJQaw6QOpy+mVMZBA0EQGoaLqMfecbceskz2ocJvIVgiiKotRFDJRer4darYZOp0NoaKjU5RD5jOztJfjwcBX+8+YE5CyaJHU5/fbrj47h3f3lWDpnNH5z11SpyyHyGc78/PasDjkichsWi4jdXfvwzB8fJXE1AzOva1qI+woRuS8GFiLqlytvZ06L9+yVqW8YOwx+MgFljW242GiQuhwi6gEDCxH1i2105cbEYR53O/P3haj8MWO0NXRxlIXIPXn2dxkiksyesw0AuqdTPJ3tbqHd3zVIXAkR9YSBhYicZjB24nC5dcPAuYmRElfjGvPGWQNL4bkGmDq5ezORu2FgISKnHShrQodZxMjwAIyKCJS6HJeYEheKYUEKGExm7t5M5IYYWIjIaf86Y502mZsY6TG7M1+PTCbgxq7Ror3nOC1E5G4YWIjIabb+lRu9ZDrI5sbEYQCAf51lYCFyNwwsROSUhlYjTmlbAFhvB/YmN4y1BrAjlTq0GjslroaIrsTAQkRO2XuuEQAwOTYUw4K9a/sMTUQgNBEBMFtEHLjQKHU5RHQFBhYicoqtf8U2feJtbuwaZdl7loGFyJ0wsBBRn4mi6LX9KzY32BtvGViI3AkDCxH12cXGNlQ1X4a/XMCsMRFSlzMo5iRYR45O1ujRZDBJXA0R2TCwEFGf2UZXZowKR6DCT+JqBsfwECUmRIcAAPad5ygLkbtgYCGiPrOtT+Kt00E2c8by9mYid8PAQkR9Iooi9p9vAuB9tzN/ny2QFbKPhchtMLAQUZ+crWtFo8EElb8MSSPDpC5nUM0aEwGZAJxvMKBGd1nqcogIDCxE1Ee2fo7U0eFQ+Hn3tw51gD+mdYWyf/H2ZiK34N3fdYjIZfZdsE4HpY/x7ukgG9u0FxtvidwDAwsRXdeV/SuzE3wjsKR33bZ9oCuoEZG0GFiI6LrO1RvQ0GqE0k+GZI1a6nKGROrocMgEoLypjX0sRG6AgYWIrmt/1746M0aFQ+knl7iaoRGi8sfUEdZwxlEWIukxsBDRde3rmg5KT/DO1W17Myve+n5t75+IpMPAQkTXZO1fsY6w+ErDrU16V78Od24mkh4DCxFd04UGA+pajFD4yTB9VJjU5QypmfHhEARrD099i1Hqcoh8GgMLEV3T/q7+jRRNGFT+vtG/YhMWqLDvK3SwjNNCRFJiYCGia7KtQ+IrtzN/n+325v1cj4VIUgwsRNQrh/VXxvhWw62NrY9lP+8UIpIUAwsR9epiYxu0+nYo5DJMHxUudTmSmNl1p9Dp2hY0t5kkrobIdzGwEFGvbH0bSSPVCFD4Vv+KzfAQJcYOD4IoAgfLLkldDpHPYmAhol4Vl1t/QKfG++bois2srtu52cdCJJ1+BZYNGzYgPj4eKpUK6enpOHDgQK/nfvjhh0hLS0NYWBiCgoKQkpKCt99+2+EcURSxatUqxMbGIiAgABkZGThz5kx/SiMiFyq62BVYfHQ6yGZ214J5B3inEJFknA4s27dvR3Z2NlavXo3i4mIkJycjMzMTdXV1PZ4fERGBX//61ygsLMTRo0eRlZWFrKwsfPnll/ZzXn75Zbz22mvIy8vD/v37ERQUhMzMTLS3t/f/nRHRgOgud+BMXSsAYMZo3w4ss7oajo9X6dDS3iFxNUS+yenAsm7dOixfvhxZWVmYPHky8vLyEBgYiM2bN/d4/vz583H33Xdj0qRJGDt2LB5//HEkJSVhz549AKyjK+vXr8czzzyDu+66C0lJSdi6dSuqq6uxY8eOAb05Iuq/kopmiCIwelggIoOVUpcjqVh1ADQRAbCIwOHyZqnLIfJJTgUWk8mEoqIiZGRkdF9AJkNGRgYKCwuv+3xRFFFQUIDTp09j3rx5AIALFy5Aq9U6XFOtViM9Pb3XaxqNRuj1eocHEbkWp4McpY22jrIc4rQQkSScCiwNDQ0wm82Ijo52OB4dHQ2tVtvr83Q6HYKDg6FQKHD77bfj9ddfx2233QYA9uc5c83c3Fyo1Wr7Q6PROPM2iKgPirsCi69PB9mkdTUeH7rIO4WIpDAkdwmFhISgpKQEBw8exG9/+1tkZ2dj165d/b5eTk4OdDqd/VFRUeG6YokIZouIw7Y7hBhYAHSPsJRUNKPDbJG4GiLf4+fMyZGRkZDL5aitrXU4Xltbi5iYmF6fJ5PJkJiYCABISUlBaWkpcnNzMX/+fPvzamtrERsb63DNlJSUHq+nVCqhVPr2nDrRYPqutgUGkxnBSj+M79pLx9eNiwpGqMoP+vZOlNbokTQyTOqSiHyKUyMsCoUCqampKCgosB+zWCwoKCjAnDlz+nwdi8UCo9G68+mYMWMQExPjcE29Xo/9+/c7dU0ich1b/0qKJgxymSBxNe5BJhPso02HuIAc0ZBzekooOzsbmzZtwpYtW1BaWooVK1bAYDAgKysLALB06VLk5OTYz8/NzcXOnTtx/vx5lJaW4tVXX8Xbb7+Nn/70pwAAQRDwxBNP4MUXX8Qnn3yCY8eOYenSpYiLi8PixYtd8y6JyCnsX+lZWtcy/UXsYyEack5NCQHAkiVLUF9fj1WrVkGr1SIlJQX5+fn2ptny8nLIZN05yGAw4NFHH0VlZSUCAgIwceJEvPPOO1iyZIn9nKeeegoGgwGPPPIImpubMXfuXOTn50OlUrngLRKRs4rYv9Ij+wjLxSaIoghB4OgT0VARRFEUpS5ioPR6PdRqNXQ6HUJDQ6Uuh8ijNbQakfbiPwAAR1YvgDrAX+KK3MdlkxlJz3+JDrOIb5+6BZqIQKlLIvJozvz85l5CROTANh00PjqYYeV7AhRyTIlTA7COshDR0GFgISIHnA66tjQ23hJJgoGFiBzYG265wm2PbI23DCxEQ4uBhYjsTJ0WHKnUAeAIS29sX5fv6lqgu8yNEImGCgMLEdmdrNHD1GlBeKA/xkQGSV2OWxoeokT8sECIIlBczlEWoqHCwEJEdkVXTAfxlt3edU8LsfGWaKgwsBCRHReM6xs23hINPQYWIrKzjbCwf+XabDs3H6lshqmTGyESDQUGFiICAFQ3X4ZW3w65TEDSSLXU5bi1hMhghAX6o73DghPVOqnLIfIJDCxEBKB7dGVybCgCFU7v2uFTZDLBPi3EfYWIhgYDCxEB4HSQs1JHcz0WoqHEwEJEALpv0WXDbd/Ygl1x+SV4wZZsRG6PgYWIcNlkxslqPQCOsPRV0kg1/GQC6lqMqGq+LHU5RF6PgYWIcLSyGZ0WEdGhSsSpVVKX4xFU/nJMjrPuLltc3ixtMUQ+gIGFiBw2POSCcX1n22+pmI23RIOOgYWIuOFhP00fFQYAOMwl+okGHQMLkY8TRdE+pcH+FefYAt6Jaj3aO8wSV0Pk3RhYiHxcWWMbmgwmKPxkmBLHBeOcMTI8AMNDlOi0iDhWxQXkiAYTAwuRj7Otv5I0Qg2FH78lOEMQBMzomhbiAnJEg4vfnYh8HBeMGxg23hINDQYWIh/HHZoHZoZ9AblmLiBHNIgYWIh8mL69A9/VtQDgHUL9NW2EdQG5hlYjKi9xATmiwcLAQuTDSsqbIYrAqIhADA9RSl2OR1L5yzHFvoAcp4WIBgsDC5EPY/+Ka9inhdjHQjRoGFiIfBg3PHQNe+Mtl+gnGjQMLEQ+ymwRcdi2YBz7VwbEFvhKa/S4bOICckSDgYGFyEedqWtBq7ETQQo5JsSESF2OR4tTqxAdal1A7mhls9TlEHklBhYiH2XrX0kZFQa5jBseDoR1ATlOCxENJgYWIh9lb7jldJBLdAcWNt4SDQYGFiIfxQXjXGvG6DAA1q8rF5Ajcj0GFiIf1NhqRFljGwBgOkdYXGJKnBr+cgGNBhPKm9qkLofI6/QrsGzYsAHx8fFQqVRIT0/HgQMHej1306ZNuOmmmxAeHo7w8HBkZGRcdf5DDz0EQRAcHgsXLuxPaUTUB7Y+i3FRwVAH+EtbjJewLiBn3e2a00JErud0YNm+fTuys7OxevVqFBcXIzk5GZmZmairq+vx/F27duGBBx7A119/jcLCQmg0GixYsABVVVUO5y1cuBA1NTX2x1/+8pf+vSMiui4uGDc4ujdCbJa2ECIv5HRgWbduHZYvX46srCxMnjwZeXl5CAwMxObNm3s8/91338Wjjz6KlJQUTJw4EW+++SYsFgsKCgoczlMqlYiJibE/wsP5jZRosLB/ZXDY+1g4wkLkck4FFpPJhKKiImRkZHRfQCZDRkYGCgsL+3SNtrY2dHR0ICIiwuH4rl27EBUVhQkTJmDFihVobGzs9RpGoxF6vd7hQUR9Y+q04EjXWiEcYXEt2wjLKW0L2kydEldD5F2cCiwNDQ0wm82Ijo52OB4dHQ2tVtuna/zqV79CXFycQ+hZuHAhtm7dioKCAqxZswa7d+/GokWLYDb3vGJkbm4u1Gq1/aHRaJx5G0Q+rbRGD2OnBWGB/kiIDJK6HK8SFxaAmFAVzBYRRyp0UpdD5FWG9C6hl156Cdu2bcNHH30ElUplP37//ffjzjvvxLRp07B48WJ89tlnOHjwIHbt2tXjdXJycqDT6eyPioqKIXoHRJ7P1r8yY1Q4BIELxrkap4WIBodTgSUyMhJyuRy1tbUOx2traxETE3PN565duxYvvfQSvvrqKyQlJV3z3ISEBERGRuLs2bM9fl6pVCI0NNThQUR9U1TOhtvBZJsWOszAQuRSTgUWhUKB1NRUh4ZZWwPtnDlzen3eyy+/jBdeeAH5+flIS0u77utUVlaisbERsbGxzpRHRH1QfMUIC7merZG5uLyZC8gRuZDTU0LZ2dnYtGkTtmzZgtLSUqxYsQIGgwFZWVkAgKVLlyInJ8d+/po1a/Dss89i8+bNiI+Ph1arhVarRWtrKwCgtbUVTz75JPbt24eysjIUFBTgrrvuQmJiIjIzM130NokIAKqbL6NG1w65TECyRi11OV5pSlwoFHIZmgwmXGzkAnJEruLn7BOWLFmC+vp6rFq1ClqtFikpKcjPz7c34paXl0Mm685BGzduhMlkwr333utwndWrV+O5556DXC7H0aNHsWXLFjQ3NyMuLg4LFizACy+8AKVSOcC3R0RXsvVVTIoNQaDC6X/+1AdKPzmmjghFcXkzii5eQjwbm4lcol/fsVauXImVK1f2+LnvN8qWlZVd81oBAQH48ssv+1MGETmJGx4OjRmjwlFc3ozi8ku4J3Wk1OUQeQXuJUTkQ7hg3NC4so+FiFyDgYXIR7R3mHGi2rrIIu8QGly2hubTWj1ajVxAjsgVGFiIfMTRSh06LSKiQpQYERYgdTleLUatwoiwAFhE4GhFs9TlEHkFBhYiH3HlhodcMG7wTR8VBqD7605EA8PAQuQjuEPz0LLv3MwF5IhcgoGFyAeIomj/wcmG26FhC4aHK5phsXABOaKBYmAh8gEXG9vQZDBB4SfDlDhuZTEUJsWGQuknQ3NbB843GKQuh8jjMbAQ+QDbdNC0EWoo/eQSV+MbFH4yJI20ribMaSGigWNgIfIB3PBQGrbpN26ESDRwDCxEPoAbHkrD9vXmnUJEA8fAQuTl9O0dOF3bAgCYMTpM2mJ8jC2wnKlrhb69Q+JqiDwbAwuRlztS0QxRBDQRAYgKUUldjk8ZHqLEqIhAiCJQwmX6iQaEgYXIy3HDQ2nN4AJyRC7BwELk5bhgnLRSR3MBOSJXYGAh8mIWi2ifiuCCcdKY3jWyVVLOBeSIBoKBhciLnalrRYuxE0EKOSZEh0hdjk+aGBOCQIUcLcZOnKlrlbocIo/FwELkxWzTQcmaMPjJ+c9dCn5yGZJHhgHgtBDRQPA7GJEXY/+Ke7DdTs7GW6L+Y2Ah8mLc8NA9cOdmooFjYCHyUk0GEy50bbo3Q8PAIiVb4+35egMuGUwSV0PkmRhYiLyUbTn+xKhgqAP9Ja7Gt0UEKZAQGQQAOFzBURai/mBgIfJS9g0PuWCcW7BNyxVfbJa2ECIPxcBC5KXYcOte2MdCNDAMLEReqMNswdHKZgBsuHUXtjuFSiqa0Wm2SFsMkQdiYCHyQqU1erR3WBAW6G/vnSBpjYsKQYjSD20ms333bCLqOwYWIi90qMw67TBdEwaZTJC4GgIAuUxAStdGiMXcuZnIaQwsRF7I1nCbFh8hcSV0JdvtzcVcQI7IaQwsRF5GFEUUdY2wzOAdQm6FOzcT9R8DC5GXqWq+DK2+3ToFoQmTuhy6gu3/x8XGNjS0GqUthsjDMLAQeRnb7cxT4kIRoJBLXA1dSR3gj3FRwQA4LUTkLAYWIi/D9VfcW/e0ULO0hRB5mH4Flg0bNiA+Ph4qlQrp6ek4cOBAr+du2rQJN910E8LDwxEeHo6MjIyrzhdFEatWrUJsbCwCAgKQkZGBM2fO9Kc0Ip9nCyxpo9lw645msPGWqF+cDizbt29HdnY2Vq9ejeLiYiQnJyMzMxN1dXU9nr9r1y488MAD+Prrr1FYWAiNRoMFCxagqqrKfs7LL7+M1157DXl5edi/fz+CgoKQmZmJ9vb2/r8zIh/UauxEaY0eAEdY3JVtIb+jVc3o4AJyRH3mdGBZt24dli9fjqysLEyePBl5eXkIDAzE5s2bezz/3XffxaOPPoqUlBRMnDgRb775JiwWCwoKCgBYR1fWr1+PZ555BnfddReSkpKwdetWVFdXY8eOHQN6c0S+pqS8GRYRGBEWgBi1SupyqAcJkUFQB/ijvcNiD5dEdH1OBRaTyYSioiJkZGR0X0AmQ0ZGBgoLC/t0jba2NnR0dCAiwjpcfeHCBWi1WodrqtVqpKen93pNo9EIvV7v8CAi9q94AplMwPSuBeSKOC1E1GdOBZaGhgaYzWZER0c7HI+OjoZWq+3TNX71q18hLi7OHlBsz3Pmmrm5uVCr1faHRqNx5m0Qea1DF5sAAGnxDCzuLHUUG2+JnDWkdwm99NJL2LZtGz766COoVP0frs7JyYFOp7M/KioqXFglkWcyW0Qc7voByBEW92brY2HjLVHfORVYIiMjIZfLUVtb63C8trYWMTEx13zu2rVr8dJLL+Grr75CUlKS/bjtec5cU6lUIjQ01OFB5Ou+q21Bq7ETQQo5JkSHSF0OXUOyJgwywbrIX62eNxcQ9YVTgUWhUCA1NdXeMAvA3kA7Z86cXp/38ssv44UXXkB+fj7S0tIcPjdmzBjExMQ4XFOv12P//v3XvCYROTrU9dv69FHh8JNziSV3Fqz0w4QY6y9aHGUh6hunv6tlZ2dj06ZN2LJlC0pLS7FixQoYDAZkZWUBAJYuXYqcnBz7+WvWrMGzzz6LzZs3Iz4+HlqtFlqtFq2trQAAQRDwxBNP4MUXX8Qnn3yCY8eOYenSpYiLi8PixYtd8y6JfIDtB98MTgd5hNTRYQC6gyYRXZufs09YsmQJ6uvrsWrVKmi1WqSkpCA/P9/eNFteXg6ZrDsHbdy4ESaTCffee6/DdVavXo3nnnsOAPDUU0/BYDDgkUceQXNzM+bOnYv8/PwB9bkQ+Rp7wy0Di0eYGR+Bd/aV41BZk9SlEHkEQRRFUeoiBkqv10OtVkOn07GfhXxSnb4ds/63AIIAHFm9AKEqf6lLouuoar6MG1/6J+QyAceeW4BAhdO/PxJ5PGd+fnOim8gL2NbzmBAdwrDiIUaEBSBOrYLZIqKEtzcTXRcDC5EXsPVBcP0Vz5IWb11A82AZ+1iIroeBhcgLHOIKtx5pZlfAtPUfEVHvGFiIPFx7hxknqnQAuEOzp7GNsBRfvIROboRIdE0MLEQe7khFMzotIoaHKDEyPEDqcsgJ46NDEKLyg8Fkxilti9TlELk1BhYiD1dU3tW/MjocgiBIXA05Qy4T7LehH+TtzUTXxMBC5OGKyti/4sm6G28ZWIiuhYGFyINZLOIVdwixf8UTzbziTiEvWBaLaNAwsBB5sO/qWqC73IFAhRxT4rhooidKGqmGQi5DfYsR5U1tUpdD5LYYWIg82IEL1mmEGaPC4c8NDz2Syl+OaSPVALgeC9G18DsckQezBZaZnA7yaLYF/7ivEFHvGFiIPJQoivZGzVljGFg82czRbLwluh4GFiIPVd7Uhlq9Ef5yAdNHhUldDg2A7Q6vc/UGNLYaJa6GyD0xsBB5KNt0UNLIMKj85RJXQwMRHqTA+OhgAN0bWRKRIwYWIg/F/hXvYrst/RADC1GPGFiIPFR3/woXjPMGto0Q2cdC1DMGFiIPVKdvR1ljGwQBSOWGh17BtnHl8SodLpvMEldD5H4YWIg80IGu38InxoRCHeAvcTXkCiPDAxATqkKHWURJRbPU5RC5HQYWIg90sKt/JZ23M3sNQRDs67HY+pOIqBsDC5EH2s+GW6+UnjAMALD/QqPElRC5HwYWIg+ju9yB07UtAICZbLj1KrO7RsyKyy/B1GmRuBoi98LAQuRhii42QRSBMZFBiApRSV0OuVBiVDCGBSnQ3mHB0cpmqcshcisMLEQepns6iKMr3kYQBKQnWEdZ9p3ntBDRlRhYiDyMreF21phhEldCgyF9jK2PhY23RFdiYCHyIJdNZhyt1AEAZrHh1ivN7mq8PVR2CR1m9rEQ2TCwEHmQwxWX0GkRER2qhCYiQOpyaBCMiwpGeKA/Lnd0h1MiYmAh8ij7zln7GmYnDIMgCBJXQ4NBJhMwq+tuId7eTNSNgYXIgxR2NWLOSWD/ijezTQvtO88+FiIbBhYiD3HZZLYv2T5nLAOLN7M13haVNaGTfSxEABhYiDzGoYtN6DCLiFOrMCoiUOpyaBBNjAmBOsAfBpMZx6v1UpdD5BYYWIg8RKGtf2Us+1e83ZV9LFyPhciqX4Flw4YNiI+Ph0qlQnp6Og4cONDruSdOnMA999yD+Ph4CIKA9evXX3XOc889B0EQHB4TJ07sT2lEXov9K77FtrHlfgYWIgD9CCzbt29HdnY2Vq9ejeLiYiQnJyMzMxN1dXU9nt/W1oaEhAS89NJLiImJ6fW6U6ZMQU1Njf2xZ88eZ0sj8lqtxk77La7sX/ENtsbbg2WX2MdChH4ElnXr1mH58uXIysrC5MmTkZeXh8DAQGzevLnH82fOnIlXXnkF999/P5RKZa/X9fPzQ0xMjP0RGRnpbGlEXutgWRPMFhGaiACMDGf/ii+YFBuKEJUfWo2dOFnDPhYipwKLyWRCUVERMjIyui8gkyEjIwOFhYUDKuTMmTOIi4tDQkICHnzwQZSXl/d6rtFohF6vd3gQeTPb+iucDvIdcplgX82YfSxETgaWhoYGmM1mREdHOxyPjo6GVqvtdxHp6el46623kJ+fj40bN+LChQu46aab0NLS0uP5ubm5UKvV9odGo+n3axN5Anv/CqeDfIrt//e/zjKwELnFXUKLFi3Cfffdh6SkJGRmZuKLL75Ac3Mz/vrXv/Z4fk5ODnQ6nf1RUVExxBUTDR19eweOV3X1ryRwqtSX3DDW+v/7wIUmmDrZx0K+zc+ZkyMjIyGXy1FbW+twvLa29poNtc4KCwvD+PHjcfbs2R4/r1Qqr9kPQ+RNDpxvgkUExkQGIUatkrocGkITY0IQEaRAk8GEkopm+63ORL7IqREWhUKB1NRUFBQU2I9ZLBYUFBRgzpw5LiuqtbUV586dQ2xsrMuuSeSpbNNBs9m/4nNkMgE32KeFGiSuhkhaTk8JZWdnY9OmTdiyZQtKS0uxYsUKGAwGZGVlAQCWLl2KnJwc+/kmkwklJSUoKSmByWRCVVUVSkpKHEZPfvnLX2L37t0oKyvD3r17cffdd0Mul+OBBx5wwVsk8my2BePYv+Kbbky0TgvtPcfAQr7NqSkhAFiyZAnq6+uxatUqaLVapKSkID8/396IW15eDpmsOwdVV1dj+vTp9o/Xrl2LtWvX4uabb8auXbsAAJWVlXjggQfQ2NiI4cOHY+7cudi3bx+GDx8+wLdH5NkuGUz2W1pnJ3A6wBfd2NXHcri8GQZjJ4KUTn/bJvIKgiiKotRFDJRer4darYZOp0NoaKjU5RC5TP7xGvz8nWIkRgXjH9k3S10OSWTumn+i8tJl/PmhmbhlYpTU5RC5jDM/v93iLiEi6tm3Z6zTAHMTeXeQL7ONsrCPhXwZAwuRG9tzloGFgBsSuxpvz3E9FvJdDCxEbqq8sQ0XG9vgJxMwmw23Ps22HktpjR6NrUaJqyGSBgMLkZv69mw9AGD6qDAEs9HSpw0PUWJiTAiA7tvciXwNAwuRm9rT1b9y0zjeLUfdoyxcpp98FQMLkRsyW0R7g+XccexfIeDGRC4gR76NgYXIDR2tbIa+vRMhKj8kjVBLXQ65gfSEYZDLBJQ3taGiqU3qcoiGHAMLkRuyTQfdMHYY/OT8Z0pAsNIPqaPCAQC7v6uXuBqiocfvhERu6Nuz7F+hq80bb50eZGAhX8TAQuRmWo2dOFx+CQBwE/tX6Ao3j7euclt4rhGmTovE1RANLQYWIjez/3wjOswiNBEBGD0sSOpyyI1MiQvFsCAFWo2dKO4KtUS+goGFyM10L8fP6SByJJMJ9lG3bzgtRD6GgYXIzdiW45/H6SDqwbzx1iDLPhbyNQwsRG6k8lIbzta1QiZ0LxRGdCVbI/aJaj3qW7hMP/kOBhYiN7LrtPW35tTR4VAH+ktcDbmj4SFKTIkLBQB8e4ajLOQ7GFiI3Miu03UAgPkToiSuhNzZzZwWIh/EwELkJto7zPZ9YuZPYMMt9c7Wx/LtmQZYLKLE1RANDQYWIjdxsKwJlzvMiApRYnJsqNTlkBubMSocwUo/NBlMOF6tk7ocoiHBwELkJr4+ZR3ev2VCFARBkLgacmcKPxnmjLVuhsjbm8lXMLAQuQlb/8otEzkdRNdn62P5+jQDC/kGBhYiN3Cx0YDzDQb4yQTcmMjbmen6bplobcwuLr+EJoNJ4mqIBh8DC5EbsN3OnBYfjhAVb2em6xsRFoBJsaEQReDrU3VSl0M06BhYiNzA17bpIN7OTE7ImGT9+/JPBhbyAQwsRBK7bDKj8Jz1dmbbMD9RX/yg6+/L7u/quXszeT0GFiKJ7TnbAGOnBSPCAjAuKljqcsiDJI8MQ2SwEq3GThwsa5K6HKJBxcBCJLGdJ7UAgNsmR/N2ZnKKTCbgB113lf2jtFbiaogGFwMLkYTMFhEFpdb+g9smR0tcDXmiH0y0/r0pKK2DKHLVW/JeDCxEEiqpuIRGgwkhKj/MGhMhdTnkgW4aFwmFXIbypjacq2+VuhyiQcPAQiShr05ah/FvmRAFfzn/OZLzgpR+9lVv/1HKu4XIe/E7JJGEdnYFFk4H0UDc2nV7cwH7WMiLMbAQSeRcfSvO1xvgLxe4OzMNSMYka+A9dPES6luMEldDNDj6FVg2bNiA+Ph4qFQqpKen48CBA72ee+LECdxzzz2Ij4+HIAhYv379gK9J5A1soyuzE4ZxdVsakLiwACSPVEMUu/9eEXkbpwPL9u3bkZ2djdWrV6O4uBjJycnIzMxEXV3Pc6dtbW1ISEjASy+9hJiYGJdck8gb2H6wLOB0ELlA5lTr99f8E1qJKyEaHE4HlnXr1mH58uXIysrC5MmTkZeXh8DAQGzevLnH82fOnIlXXnkF999/P5RKpUuuSeTpGlqNKC6/BADIYGAhF1g4xRpY9p5tgO5yh8TVELmeU4HFZDKhqKgIGRkZ3ReQyZCRkYHCwsJ+FdCfaxqNRuj1eocHkSf56kQtRBGYNkKNWHWA1OWQF0gYHozx0cHotIj45ylOC5H3cSqwNDQ0wGw2Izra8TfC6OhoaLX9G4bszzVzc3OhVqvtD41G06/XJpLKF8dqAACLpvU8TUrUH7ZRlvzjnBYi7+ORdwnl5ORAp9PZHxUVFVKXRNRnTQYTCs9bNzu8fVqsxNWQN7H1sez+rh5tpk6JqyFyLacCS2RkJORyOWprHYcba2tre22oHYxrKpVKhIaGOjyIPMWXJ7QwW0RMiQvF6GFBUpdDXmRybChGRQSivcOC3afrpS6HyKWcCiwKhQKpqakoKCiwH7NYLCgoKMCcOXP6VcBgXJPIndmmg37I0RVyMUEQsJB3C5GX8nP2CdnZ2Vi2bBnS0tIwa9YsrF+/HgaDAVlZWQCApUuXYsSIEcjNzQVgbao9efKk/b+rqqpQUlKC4OBgJCYm9umaRN6iyWDC3nOcDqLBkzklBn/85jwKSuvQ3mGGyl8udUlELuF0YFmyZAnq6+uxatUqaLVapKSkID8/3940W15eDpmse+Cmuroa06dPt3+8du1arF27FjfffDN27drVp2sSeYudJ63TQZNjQxEfyekgcr3pmjDEqlWo0bVj1+l6+4gLkacTRC/Yj1yv10OtVkOn07Gfhdza0s0H8M139XgycwIeuyVR6nLIS/3285PY9O0F3J4Uiw0/mSF1OUS9cubnt0feJUTkiZrbTNh7tgEA+1docN2ZPAKAdTNEg5F3C5F3YGAhGiJfntCi0yJiUmwoxnA6iAbR1BHWv2PtHRbuLUReg4GFaIjsOFwNAPhREkdXaHAJgoA7uv6efXKkWuJqiFyDgYVoCFQ3X8a+C9a7gxZPHyFxNeQL7kyJAwB88109LhlMEldDNHAMLERD4JMj1RBFIH1MBEaEce8gGnyJUSGYFBuKTouIv3OpfvICDCxEQ2DH4SoAwN0cXaEhdGeydZTlkyNVEldCNHAMLESD7GS1Hqe0LVDIZVjEu4NoCN2RbP37tv9CE7S6domrIRoYBhaiQbajxPrb7a2ToqAO8Je4GvIlI8MDMTM+HKIIfHi4UupyiAaEgYVoEJktIj7uCixstiUp3Js6EgDwQVElvGCdUPJhDCxEg2jf+UbU6o1QB/hj/oThUpdDPuj2pDgE+Mtxvt6A4vJmqcsh6jcGFqJB9Lci6zD8D6fFQunHTeho6AUr/bBomnU/oQ+KKiSuhqj/GFiIBonucge+OF4DALgvbaTE1ZAvs00LfXakBpdNZomrIeofBhaiQfLJkWq0d1gwPjoY0zVhUpdDPmz2mGEYGR6AFmMnvjzBNVnIMzGwEA2Svx60Dr//OE0DQRAkroZ8mUwm2EdZ3ue0EHkoBhaiQXC8SodjVTr4ywX82wxOB5H07un6e7j3XCMqL7VJXA2R8xhYiAbBXw9Zf4tdMCUGEUEKiashAjQRgbhh7DCIYvfoH5EnYWAhcrH2DrN9Kf77Z2okroao20/SRwEAth2sQIfZInE1RM5hYCFysc+P1kDf3okRYQG4cWyk1OUQ2S2YHIPIYCXqWozYebJW6nKInMLAQuRiWwvLAFh/m5XJ2GxL7kPhJ7OP+r2z76LE1RA5h4GFyIVKKppxpFIHhVzG6SBySw+kj4JMsDbfnqtvlbocoj5jYCFyoa17ywAAP0qOxbBgpbTFEPVgRFgAfjAxCgDw7r5yiash6jsGFiIXaWg14rOj1pVtl82Jl7YYomt4cPZoANal+ttMnRJXQ9Q3DCxELrL9YAVMZguSR6qRzJVtyY3dPG444ocFQt/ead/visjdMbAQuUCH2WJvYlzK0RVyczKZgH+fOwYA8Kc9F2CxiBJXRHR9DCxELvD50RrU6NoRGazA7UmxUpdDdF33po6EOsAfZY1t+Ecpb3Em98fAQjRAoijiD9+cBwA8dEM8VP5yiSsiur5AhZ99Ibk391yQuBqi62NgIRqgb880oLRGj0CFHD/tamYk8gTL5sTDTybgwIUmHK1slrocomtiYCEaoD92ja78OE2DsEDuG0SeI0atwh3JcQCATd9ylIXcGwML0QAcr9Jhz9kGyGUCHu5qYiTyJMtvSgAAfH60GhcaDBJXQ9Q7BhaiAbD1rtw+LRaaiECJqyFy3uS4UNw6MQoWEfj912elLoeoVwwsRP10tq4Fnx2tBgD8/OaxEldD1H8rf5AIAPjocBUqmtokroaoZ/0KLBs2bEB8fDxUKhXS09Nx4MCBa57//vvvY+LEiVCpVJg2bRq++OILh88/9NBDEATB4bFw4cL+lEY0ZH5XcBaiCGROicbkuFCpyyHqt+mjwnHTuEh0WkTk7T4ndTlEPXI6sGzfvh3Z2dlYvXo1iouLkZycjMzMTNTV1fV4/t69e/HAAw/g4YcfxuHDh7F48WIsXrwYx48fdzhv4cKFqKmpsT/+8pe/9O8dEQ2BM7XdoyuP3zpe4mqIBm7lLdZRlvcPVUKra5e4GqKrOR1Y1q1bh+XLlyMrKwuTJ09GXl4eAgMDsXnz5h7P/93vfoeFCxfiySefxKRJk/DCCy9gxowZeOONNxzOUyqViImJsT/Cw8P7946IhsBr/7SOriycEsPRFfIK6QnDMCs+AiazBW98fUbqcoiu4lRgMZlMKCoqQkZGRvcFZDJkZGSgsLCwx+cUFhY6nA8AmZmZV52/a9cuREVFYcKECVixYgUaGxt7rcNoNEKv1zs8iIbKlaMr/3XrOImrIXKd7AXW0cJtBypQxjuGyM04FVgaGhpgNpsRHR3tcDw6OhparbbH52i12uuev3DhQmzduhUFBQVYs2YNdu/ejUWLFsFsNvd4zdzcXKjVavtDo9E48zaIBmRN/mmOrpBXmp0wDDePH45Oi4h1O7+TuhwiB25xl9D999+PO++8E9OmTcPixYvx2Wef4eDBg9i1a1eP5+fk5ECn09kfFRUVQ1sw+az95xvxj9JayGUCfpk5QepyiFzuya6/158cqcaJap3E1RB1cyqwREZGQi6Xo7bWcaOs2tpaxMTE9PicmJgYp84HgISEBERGRuLs2Z7XBFAqlQgNDXV4EA02URTxv38/BQC4f6YGiVHBEldE5HpTR6hxZ9fqty/nn5a4GqJuTgUWhUKB1NRUFBQU2I9ZLBYUFBRgzpw5PT5nzpw5DucDwM6dO3s9HwAqKyvR2NiI2Fjuekvu47OjNThS0YxAhRxPZPDOIPJe2beNh59MwO7v6vHtmXqpyyEC0I8poezsbGzatAlbtmxBaWkpVqxYAYPBgKysLADA0qVLkZOTYz//8ccfR35+Pl599VWcOnUKzz33HA4dOoSVK1cCAFpbW/Hkk09i3759KCsrQ0FBAe666y4kJiYiMzPTRW+TaGCMnWa88qX1t83/nDcWw0OUEldENHjiI4PwsznWjTyf//QkOswWiSsi6kdgWbJkCdauXYtVq1YhJSUFJSUlyM/PtzfWlpeXo6amxn7+DTfcgPfeew9//OMfkZycjA8++AA7duzA1KlTAQByuRxHjx7FnXfeifHjx+Phhx9Gamoqvv32WyiV/KFA7uGPu8+jvKkNUSFKLJ/HPYPI+z2RMR4RQQqcrWvF1sKLUpdDBEEURVHqIgZKr9dDrVZDp9Oxn4VcrqKpDRnrdsPYacHv7k/BXSkjpC6JaEhsO1COpz88hhClH75+cj4ig/lLJLmWMz+/3eIuISJ39twnJ2DstGBOwjB7MyKRL7gvTYNpI9RoMXbi5fxTUpdDPo6Bhegadp6sRcGpOvjLBbyweAoEQZC6JKIhI5cJeO7OyQCAvx6qxN5zDRJXRL6MgYWoFy3tHVj9sXXPq4fnJiAxKkTiioiGXuroCDyYPgoAkPPhMVw29bygJ9FgY2Ah6sVvPy9Fta4doyIC8V+3JkpdDpFknl40EbFqFS42tuH//sEVcEkaDCxEPdh1ug7bDlpXUH7l3iQEKvwkrohIOiEqf/z2buudnW9+ex4lFc3SFkQ+iYGF6Ht0lzvw9N+OAQCyboxHesIwiSsikt4PJkbjrpQ4WEQge3sJ2kydUpdEPoaBhegKoiji2R3HodW3I35YIJ7KnCh1SURu47k7piAmVIXzDQb85tOTUpdDPoaBhegK2w5W4JMj1ZDLBLz642QEKORSl0TkNsKDFFi3JBmCYP238sWxmus/ichFGFiIupzS6vHcJycAAL9cMAGpoyMkrojI/dwwNhIrbh4LAHj6b0dR0dQmcUXkKxhYiAC0Gjvx2LvFMHZaMH/CcPznvASpSyJyW//vtvFI0YRB396J/3y7iLc605BgYCGfZ7GIeGJbCc7VGxAdqsSr9yVDJuMCcUS98ZfL8PsHZ2BYkAIna/R4+sOj8IJdXsjNMbCQz3v5y9P4R2ktFH4y5P00FcO4XwrRdcWFBeD3D86An0zAxyXV2PTtealLIi/HwEI+7W9FlcjbfQ6Adb2V6aPCJa6IyHOkJwzDsz+yLt2f+/dT+DubcGkQMbCQz9p1ug5Pf3gUALDylkTuwkzUD0vnjMaD6aMgisDj20qw73yj1CWRl2JgIZ90sKwJP3+nCB1mEXckxyH7tvFSl0TkkQRBwG/umooFk6NhMluwfOshnNLqpS6LvBADC/mc41U6/PtbB9HeYb0jiE22RAMjlwl47YHpSBsdjpb2Tjy4aT9Oa1ukLou8DAML+ZTD5Zfwk0370NLeiVnxEdj4YCoUfvxnQDRQKn85/rRsJqbEhaLRYMIDm/ZxpIVcit+pyWcUnmvET9/cD317J2aMCsObD6VxJVsiF1IH+uO9/5iNaSPUaDKY8MAf9+FYpU7qsshLMLCQT8g/XoOH/nwABpMZN4wdhrcfTkeoyl/qsoi8jjrQH+/8RzqSR6pxqa0DP/5DIf55qlbqssgLMLCQVxNFERu+Poufv2NdxTZjUhQ2PzQTQUo/qUsj8lrqAGtouWlcJC53mPEfWw7h3f0XpS6LPBwDC3mtNlMnsv96BK98eRoA8NAN8cj7aSpU/pwGIhpsISp/bH5oJu5LHQmLCPz6o+PI+fAo2ju4jD/1D3/NJK90WtuCle8V40xdK+QyAc/dMRk/mxMvdVlEPsVfLsPL9yZh9LBAvLrzO/zlQAWOVemw8cFUaCICpS6PPAxHWMirWCwi3t53EXe+sQdn6loRFaLE2w/PYlghkoggCFj5g3HY+u+zEB7oj+NVeiz63bfYfrCc+w+RUwTRC/7G6PV6qNVq6HQ6hIaGSl0OSeRCgwG/+ttRHLjQBACYN3441v04GZHcG4jILVQ3X8Z//eUwDl28BAC4ZcJw/PbuaYgLC5C4MpKKMz+/GVjI4xmMnfjDN+fxh93nYOy0IMBfjqcWTsCyOfFcEI7IzZgtIv605zzWfvUdTJ0WqPxleGx+IpbPS2B/mQ9iYCGfYLaI+FtRJdZ+dRp1LUYAwE3jIvG/d0/j/DiRmztT24Jff3QcB8qsI6KaiAA8mTkRt0+LhZy/aPgMBhbyaqZOC3YcrkLe7nM432AAAIyKCMTTiyZi0dQYCAK/2RF5AlEU8cmRauR+cQpafTsAIDEqGP916zgGFx/BwEJeqclgwgdFFfjzv8pQo7N+c1MH+GPlLYlYesNoKP04nEzkiQzGTrz57QX8ac956Ns7AQCjhwXiZ7NH4740DdQBXOTRWzGwkNfoNFuw/0ITth+sQP5xLUxmCwBgeIgSy28ag5+kj0YwF4Ej8gr69g689a8y/GnPBegudwAAAvzluCM5FotTRiA9YRhHXbwMAwt5tA6zBQcuNOHzYzX48rgWjQaT/XPTRqjxYPooLJ4+gg16RF6qzdSJHYersbWwDKeu2PU5KkSJHyXFYcGUaKSODoe/nCtzeDoGFvIoFouIs/Wt2HOmAXvONmD/+UYYTN2rYYYH+mPRtFg8MHMUpo1US1gpEQ0lURRx6OIlfFhchS+O1dhHXQAgROmHGxMjMW/8cMyMD8fY4cG8K9ADDXpg2bBhA1555RVotVokJyfj9ddfx6xZs3o9//3338ezzz6LsrIyjBs3DmvWrMEPf/hD++dFUcTq1auxadMmNDc348Ybb8TGjRsxbty4PtXDwOI5LBYRVc2XcaJahyOVOhytbMbRSh1auuatbYYFKXDb5Gj8cFos5owdxt+kiHycqdOCb76rx+fHavDNd/UOI68AEKryw4zR4ZiuCcfE2BBMjAmBJjyQIcbNDWpg2b59O5YuXYq8vDykp6dj/fr1eP/993H69GlERUVddf7evXsxb9485Obm4kc/+hHee+89rFmzBsXFxZg6dSoAYM2aNcjNzcWWLVswZswYPPvsszh27BhOnjwJlUrl0jdMg6+9w4xafTuqm9uh1V9GWUMbztW34ly9ARcaWtHeYbnqOSp/GWbGR2BuYiTmjovEpJhQfqMhoh5ZLCKOVemw63Q99p1vRElFMy73sEdRoEKOcdEhGBsZhJERgRgVEQhNeAA0EYGIClHCj78ISW5QA0t6ejpmzpyJN954AwBgsVig0Wjwi1/8Ak8//fRV5y9ZsgQGgwGfffaZ/djs2bORkpKCvLw8iKKIuLg4/Pd//zd++ctfAgB0Oh2io6Px1ltv4f7773fpG6brs1hEtHea0WYy47LJ+mebqROXO6wfN7d1oPlyB5rbTLjUZrJ+3NaBRoMJtfp2NH3vN5/v85cLSIwKQfJINZJGhiFppBoTYkI4ikJE/dJhtuBUTQuKLjbhaKUOp7QtOFvfClPn1b8c2QgCEB6oQGSwApHBSgwPUSIyWIlQlT9CVH5dD3+Edv0ZrPJDoEIOlZ8cSn8ZFHIZf6lyAWd+fjt1e4XJZEJRURFycnLsx2QyGTIyMlBYWNjjcwoLC5Gdne1wLDMzEzt27AAAXLhwAVqtFhkZGfbPq9VqpKeno7CwsMfAYjQaYTQa7R/r9Xpn3kafdZotePHzUvvHoihCtP83YPvI+t/dx3HF8euda7+iw3HRdqj7Gt873v000eF1rjxmtojosIjoNFvQecWfHWYRZosFnWYRHV1/2j5/ucPc4wiIs1T+MsSpAxCjVkETHoixUUEYOzwYY4cHY2R4AH+zISKX8ZfLMG2k2qHHrdNsQVmjAae1rbjYZEBFUxsqmi6j4lIbqi5dRqdFRJPBhCaDCd/VtvbrdRVyGZT+Mij95FD6Wf/bXyaDXCZc9fC78mPB8XOyrrWjBAEQYN1/yR6FBECAYP9c93ldx644sfv59iMO1xwof7mAX98+ecDX6S+nAktDQwPMZjOio6MdjkdHR+PUqVM9Pker1fZ4vlartX/edqy3c74vNzcXzz//vDOl94tZFPHW3rJBfx13pvKXIVDhhwB/OQIUcgQq5FAH+EMd4I/wQAXCA/0RFqhAeJD1z5hQFWLVKqgD/LmAGxFJxk8uQ2JUCBKjQq76nNki4lKbCQ2tRjS0mFDf2o6GFhMaDEboL3eipb0DLe1X/mn978sdZliumJMwmS0wmS1oQedVr+GNFH4yzwks7iInJ8dh1Eav10Oj0bj8dfxkMjx2y1gA3UnV+t+wR9jvJ97u/77i+BU/uL+ffG3X6Om49Xyhh3OuOH7Fa+GKVC4IgJ9MgJ9MBj9595/+tv+WCfCTdx3r+o3AXy5AdUUwUfnJOeRJRF5HLhMQGWydAkKMc8/tMFtg7LTA2GG2/tlpgbHTOjLd3mGG2WIdsbZ0/Wm2PUTryLbZAoc/Oy2ifeTdPor+vdFysYdj+N75InoZzb9iZuBa+tIcIvXPA6cCS2RkJORyOWprax2O19bWIiam5//rMTEx1zzf9mdtbS1iY2MdzklJSenxmkqlEkrl4O/AK5cJeDJz4qC/DhEReQZ/uQz+chkXrJSAU40ECoUCqampKCgosB+zWCwoKCjAnDlzenzOnDlzHM4HgJ07d9rPHzNmDGJiYhzO0ev12L9/f6/XJCIiIt/idETMzs7GsmXLkJaWhlmzZmH9+vUwGAzIysoCACxduhQjRoxAbm4uAODxxx/HzTffjFdffRW33347tm3bhkOHDuGPf/wjAOvUxhNPPIEXX3wR48aNs9/WHBcXh8WLF7vunRIREZHHcjqwLFmyBPX19Vi1ahW0Wi1SUlKQn59vb5otLy+HTNY9cHPDDTfgvffewzPPPIP/+Z//wbhx47Bjxw77GiwA8NRTT8FgMOCRRx5Bc3Mz5s6di/z8/D6twUJERETej0vzExERkSSc+fnNxTCIiIjI7TGwEBERkdtjYCEiIiK3x8BCREREbo+BhYiIiNweAwsRERG5PQYWIiIicnsMLEREROT2GFiIiIjI7XnFdpO2xXr1er3ElRAREVFf2X5u92XRfa8ILC0tLQAAjUYjcSVERETkrJaWFqjV6mue4xV7CVksFlRXVyMkJASCIEhdjuT0ej00Gg0qKiq4t9Ig4td5aPDrPHT4tR4a/Dp3E0URLS0tiIuLc9g4uSdeMcIik8kwcuRIqctwO6GhoT7/j2Eo8Os8NPh1Hjr8Wg8Nfp2trjeyYsOmWyIiInJ7DCxERETk9hhYvJBSqcTq1auhVCqlLsWr8es8NPh1Hjr8Wg8Nfp37xyuabomIiMi7cYSFiIiI3B4DCxEREbk9BhYiIiJyewwsRERE5PYYWHyE0WhESkoKBEFASUmJ1OV4nbKyMjz88MMYM2YMAgICMHbsWKxevRomk0nq0jzehg0bEB8fD5VKhfT0dBw4cEDqkrxKbm4uZs6ciZCQEERFRWHx4sU4ffq01GV5vZdeegmCIOCJJ56QuhSPwcDiI5566inExcVJXYbXOnXqFCwWC/7whz/gxIkT+L//+z/k5eXhf/7nf6QuzaNt374d2dnZWL16NYqLi5GcnIzMzEzU1dVJXZrX2L17Nx577DHs27cPO3fuREdHBxYsWACDwSB1aV7r4MGD+MMf/oCkpCSpS/EovK3ZB/z9739HdnY2/va3v2HKlCk4fPgwUlJSpC7L673yyivYuHEjzp8/L3UpHis9PR0zZ87EG2+8AcC6b5hGo8EvfvELPP300xJX553q6+sRFRWF3bt3Y968eVKX43VaW1sxY8YM/P73v8eLL76IlJQUrF+/XuqyPAJHWLxcbW0tli9fjrfffhuBgYFSl+NTdDodIiIipC7DY5lMJhQVFSEjI8N+TCaTISMjA4WFhRJW5t10Oh0A8O/uIHnsscdw++23O/y9pr7xis0PqWeiKOKhhx7Cz3/+c6SlpaGsrEzqknzG2bNn8frrr2Pt2rVSl+KxGhoaYDabER0d7XA8Ojoap06dkqgq72axWPDEE0/gxhtvxNSpU6Uux+ts27YNxcXFOHjwoNSleCSOsHigp59+GoIgXPNx6tQpvP7662hpaUFOTo7UJXusvn6tr1RVVYWFCxfivvvuw/LlyyWqnMh5jz32GI4fP45t27ZJXYrXqaiowOOPP453330XKpVK6nI8EntYPFB9fT0aGxuveU5CQgJ+/OMf49NPP4UgCPbjZrMZcrkcDz74ILZs2TLYpXq8vn6tFQoFAKC6uhrz58/H7Nmz8dZbb0Em4+8E/WUymRAYGIgPPvgAixcvth9ftmwZmpub8fHHH0tXnBdauXIlPv74Y3zzzTcYM2aM1OV4nR07duDuu++GXC63HzObzRAEATKZDEaj0eFzdDUGFi9WXl4OvV5v/7i6uhqZmZn44IMPkJ6ejpEjR0pYnfepqqrCLbfcgtTUVLzzzjv85uMC6enpmDVrFl5//XUA1imLUaNGYeXKlWy6dRFRFPGLX/wCH330EXbt2oVx48ZJXZJXamlpwcWLFx2OZWVlYeLEifjVr37FKbg+YA+LFxs1apTDx8HBwQCAsWPHMqy4WFVVFebPn4/Ro0dj7dq1qK+vt38uJiZGwso8W3Z2NpYtW4a0tDTMmjUL69evh8FgQFZWltSleY3HHnsM7733Hj7++GOEhIRAq9UCANRqNQICAiSuznuEhIRcFUqCgoIwbNgwhpU+YmAhcoGdO3fi7NmzOHv27FVhkIOY/bdkyRLU19dj1apV0Gq1SElJQX5+/lWNuNR/GzduBADMnz/f4fif//xnPPTQQ0NfEFEvOCVEREREbo8dgUREROT2GFiIiIjI7TGwEBERkdtjYCEiIiK3x8BCREREbo+BhYiIiNweAwsRERG5PQYWIiIicnsMLEREROT2GFiIiIjI7TGwEBERkdtjYCEiIiK39/8B3CcqUxjNj5sAAAAASUVORK5CYII=",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -345,7 +345,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -354,7 +354,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -363,17 +363,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([-0.66040796,  1.6221566 ,  0.78103376, -0.03896793, -0.3957174 ,\n",
-       "       -0.46236667,  0.84517539, -1.7958585 ,  1.48547635, -0.66616848])"
+       "array([-1.33191077,  0.69565932,  0.78581935,  0.07258   ,  0.10255307,\n",
+       "       -0.11553274, -1.24520828, -0.92858056,  1.91824603, -0.61798529])"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -385,7 +385,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -396,25 +396,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Counter({0.49595807013821813: 1,\n",
-       "         0.5117196913920876: 1,\n",
-       "         -0.1187083785680289: 1,\n",
-       "         -0.42015424355188685: 1,\n",
-       "         0.17241512275781976: 1,\n",
-       "         0.8689004192136313: 1,\n",
-       "         0.8474101187732266: 1,\n",
-       "         0.8250639756474332: 1,\n",
-       "         -0.9238044728907774: 1,\n",
-       "         -0.39901959000095666: 1})"
+       "Counter({1.0224897069033798: 1,\n",
+       "         0.7651630423923974: 1,\n",
+       "         0.15363056478470702: 1,\n",
+       "         0.6019226739133072: 1,\n",
+       "         0.6684496256783795: 1,\n",
+       "         -0.26645364633968444: 1,\n",
+       "         -0.23996521470021256: 1,\n",
+       "         2.1549755656324097: 1,\n",
+       "         -0.6069461510368445: 1,\n",
+       "         -0.5337576490586815: 1})"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -425,7 +425,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -433,28 +433,28 @@
       "text/html": [
        "\n",
        "<style>\n",
-       "  #altair-viz-9e4bce566532455fbe891b0998871e1d.vega-embed {\n",
+       "  #altair-viz-dcb562b6b3f845578273e3d627191a52.vega-embed {\n",
        "    width: 100%;\n",
        "    display: flex;\n",
        "  }\n",
        "\n",
-       "  #altair-viz-9e4bce566532455fbe891b0998871e1d.vega-embed details,\n",
-       "  #altair-viz-9e4bce566532455fbe891b0998871e1d.vega-embed details summary {\n",
+       "  #altair-viz-dcb562b6b3f845578273e3d627191a52.vega-embed details,\n",
+       "  #altair-viz-dcb562b6b3f845578273e3d627191a52.vega-embed details summary {\n",
        "    position: relative;\n",
        "  }\n",
        "</style>\n",
-       "<div id=\"altair-viz-9e4bce566532455fbe891b0998871e1d\"></div>\n",
+       "<div id=\"altair-viz-dcb562b6b3f845578273e3d627191a52\"></div>\n",
        "<script type=\"text/javascript\">\n",
        "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
        "  (function(spec, embedOpt){\n",
        "    let outputDiv = document.currentScript.previousElementSibling;\n",
-       "    if (outputDiv.id !== \"altair-viz-9e4bce566532455fbe891b0998871e1d\") {\n",
-       "      outputDiv = document.getElementById(\"altair-viz-9e4bce566532455fbe891b0998871e1d\");\n",
+       "    if (outputDiv.id !== \"altair-viz-dcb562b6b3f845578273e3d627191a52\") {\n",
+       "      outputDiv = document.getElementById(\"altair-viz-dcb562b6b3f845578273e3d627191a52\");\n",
        "    }\n",
        "    const paths = {\n",
        "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
        "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
-       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
+       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.17.0?noext\",\n",
        "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
        "    };\n",
        "\n",
@@ -490,19 +490,19 @@
        "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
        "    } else {\n",
        "      maybeLoadScript(\"vega\", \"5\")\n",
-       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
+       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.17.0\"))\n",
        "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
        "        .catch(showError)\n",
        "        .then(() => displayChart(vegaEmbed));\n",
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        "</script>"
       ],
       "text/plain": [
        "alt.Chart(...)"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -532,86 +532,7 @@
    "cell_type": "code",
    "execution_count": 16,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
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-       "    width: 100%;\n",
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-       "  }\n",
-       "\n",
-       "  #altair-viz-0c4d497515614344affd37223e4c331d.vega-embed details,\n",
-       "  #altair-viz-0c4d497515614344affd37223e4c331d.vega-embed details summary {\n",
-       "    position: relative;\n",
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-       "</style>\n",
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-       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
-       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
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-       "        Promise.resolve(paths[lib]) :\n",
-       "        new Promise(function(resolve, reject) {\n",
-       "          var s = document.createElement('script');\n",
-       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
-       "          s.async = true;\n",
-       "          s.onload = () => {\n",
-       "            VEGA_DEBUG[key] = version;\n",
-       "            return resolve(paths[lib]);\n",
-       "          };\n",
-       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
-       "          s.src = paths[lib];\n",
-       "        });\n",
-       "    }\n",
-       "\n",
-       "    function showError(err) {\n",
-       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
-       "      throw err;\n",
-       "    }\n",
-       "\n",
-       "    function displayChart(vegaEmbed) {\n",
-       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
-       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
-       "    }\n",
-       "\n",
-       "    if(typeof define === \"function\" && define.amd) {\n",
-       "      requirejs.config({paths});\n",
-       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
-       "    } else {\n",
-       "      maybeLoadScript(\"vega\", \"5\")\n",
-       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
-       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
-       "        .catch(showError)\n",
-       "        .then(() => displayChart(vegaEmbed));\n",
-       "    }\n",
-       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-e4e8b551560eb3334c77bcbd2c938deb.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
-       "</script>"
-      ],
-      "text/plain": [
-       "alt.Chart(...)"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "if not alt.data_transformers.active == 'json':  # Check json isn't already active\n",
     "    import os\n",
@@ -625,10 +546,16 @@
     "\n",
     "normal_values = pd.DataFrame({\"value\": n.rvs(100000)})\n",
     "\n",
-    "alt.Chart(normal_values).mark_bar().encode(\n",
+    "chart = alt.Chart(normal_values).mark_bar().encode(\n",
     "    alt.X(\"value\", bin=alt.Bin(maxbins=100)),\n",
     "    y='count()',\n",
-    ")"
+    ")\n",
+    "\n",
+    "# Display the chart\n",
+    "chart\n",
+    "\n",
+    "# Or save the chart to an HTML file\n",
+    "chart.save(\"histogram.html\")"
    ]
   },
   {
@@ -657,7 +584,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
@@ -665,28 +592,28 @@
       "text/html": [
        "\n",
        "<style>\n",
-       "  #altair-viz-40d0f0cf1bdf46f8ab89b36518488c16.vega-embed {\n",
+       "  #altair-viz-312d7b2fbe134cceb96bbdf70aaee7a9.vega-embed {\n",
        "    width: 100%;\n",
        "    display: flex;\n",
        "  }\n",
        "\n",
-       "  #altair-viz-40d0f0cf1bdf46f8ab89b36518488c16.vega-embed details,\n",
-       "  #altair-viz-40d0f0cf1bdf46f8ab89b36518488c16.vega-embed details summary {\n",
+       "  #altair-viz-312d7b2fbe134cceb96bbdf70aaee7a9.vega-embed details,\n",
+       "  #altair-viz-312d7b2fbe134cceb96bbdf70aaee7a9.vega-embed details summary {\n",
        "    position: relative;\n",
        "  }\n",
        "</style>\n",
-       "<div id=\"altair-viz-40d0f0cf1bdf46f8ab89b36518488c16\"></div>\n",
+       "<div id=\"altair-viz-312d7b2fbe134cceb96bbdf70aaee7a9\"></div>\n",
        "<script type=\"text/javascript\">\n",
        "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
        "  (function(spec, embedOpt){\n",
        "    let outputDiv = document.currentScript.previousElementSibling;\n",
-       "    if (outputDiv.id !== \"altair-viz-40d0f0cf1bdf46f8ab89b36518488c16\") {\n",
-       "      outputDiv = document.getElementById(\"altair-viz-40d0f0cf1bdf46f8ab89b36518488c16\");\n",
+       "    if (outputDiv.id !== \"altair-viz-312d7b2fbe134cceb96bbdf70aaee7a9\") {\n",
+       "      outputDiv = document.getElementById(\"altair-viz-312d7b2fbe134cceb96bbdf70aaee7a9\");\n",
        "    }\n",
        "    const paths = {\n",
        "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
        "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
-       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
+       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.17.0?noext\",\n",
        "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
        "    };\n",
        "\n",
@@ -722,12 +649,12 @@
        "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
        "    } else {\n",
        "      maybeLoadScript(\"vega\", \"5\")\n",
-       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
+       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.17.0\"))\n",
        "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
        "        .catch(showError)\n",
        "        .then(() => displayChart(vegaEmbed));\n",
        "    }\n",
-       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-1cb17f2eb89525fc84a20fbb90b4aaae.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean 1 and standard deviation 7\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
+       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-8c606c7ead9b20c5ff145411705a1ccd.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean 1 and standard deviation 7\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.17.0.json\"}, {\"mode\": \"vega-lite\"});\n",
        "</script>"
       ],
       "text/plain": [
@@ -742,28 +669,28 @@
       "text/html": [
        "\n",
        "<style>\n",
-       "  #altair-viz-01a9e97e1aaf4e49a7930536dddd0f98.vega-embed {\n",
+       "  #altair-viz-692263677ad14a3796ef9702e13f523c.vega-embed {\n",
        "    width: 100%;\n",
        "    display: flex;\n",
        "  }\n",
        "\n",
-       "  #altair-viz-01a9e97e1aaf4e49a7930536dddd0f98.vega-embed details,\n",
-       "  #altair-viz-01a9e97e1aaf4e49a7930536dddd0f98.vega-embed details summary {\n",
+       "  #altair-viz-692263677ad14a3796ef9702e13f523c.vega-embed details,\n",
+       "  #altair-viz-692263677ad14a3796ef9702e13f523c.vega-embed details summary {\n",
        "    position: relative;\n",
        "  }\n",
        "</style>\n",
-       "<div id=\"altair-viz-01a9e97e1aaf4e49a7930536dddd0f98\"></div>\n",
+       "<div id=\"altair-viz-692263677ad14a3796ef9702e13f523c\"></div>\n",
        "<script type=\"text/javascript\">\n",
        "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
        "  (function(spec, embedOpt){\n",
        "    let outputDiv = document.currentScript.previousElementSibling;\n",
-       "    if (outputDiv.id !== \"altair-viz-01a9e97e1aaf4e49a7930536dddd0f98\") {\n",
-       "      outputDiv = document.getElementById(\"altair-viz-01a9e97e1aaf4e49a7930536dddd0f98\");\n",
+       "    if (outputDiv.id !== \"altair-viz-692263677ad14a3796ef9702e13f523c\") {\n",
+       "      outputDiv = document.getElementById(\"altair-viz-692263677ad14a3796ef9702e13f523c\");\n",
        "    }\n",
        "    const paths = {\n",
        "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
        "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
-       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
+       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.17.0?noext\",\n",
        "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
        "    };\n",
        "\n",
@@ -799,12 +726,12 @@
        "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
        "    } else {\n",
        "      maybeLoadScript(\"vega\", \"5\")\n",
-       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
+       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.17.0\"))\n",
        "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
        "        .catch(showError)\n",
        "        .then(() => displayChart(vegaEmbed));\n",
        "    }\n",
-       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-4138241a11c1f79e076acebbe4cbf64c.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean 10 and standard deviation 1\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
+       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-21bddecae17d42e278e58a36d17e4062.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean 10 and standard deviation 1\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.17.0.json\"}, {\"mode\": \"vega-lite\"});\n",
        "</script>"
       ],
       "text/plain": [
@@ -819,28 +746,28 @@
       "text/html": [
        "\n",
        "<style>\n",
-       "  #altair-viz-2c42447db68d48638ed8443a283ade97.vega-embed {\n",
+       "  #altair-viz-be9820c1923e4b1a8a9166328af9c5a7.vega-embed {\n",
        "    width: 100%;\n",
        "    display: flex;\n",
        "  }\n",
        "\n",
-       "  #altair-viz-2c42447db68d48638ed8443a283ade97.vega-embed details,\n",
-       "  #altair-viz-2c42447db68d48638ed8443a283ade97.vega-embed details summary {\n",
+       "  #altair-viz-be9820c1923e4b1a8a9166328af9c5a7.vega-embed details,\n",
+       "  #altair-viz-be9820c1923e4b1a8a9166328af9c5a7.vega-embed details summary {\n",
        "    position: relative;\n",
        "  }\n",
        "</style>\n",
-       "<div id=\"altair-viz-2c42447db68d48638ed8443a283ade97\"></div>\n",
+       "<div id=\"altair-viz-be9820c1923e4b1a8a9166328af9c5a7\"></div>\n",
        "<script type=\"text/javascript\">\n",
        "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
        "  (function(spec, embedOpt){\n",
        "    let outputDiv = document.currentScript.previousElementSibling;\n",
-       "    if (outputDiv.id !== \"altair-viz-2c42447db68d48638ed8443a283ade97\") {\n",
-       "      outputDiv = document.getElementById(\"altair-viz-2c42447db68d48638ed8443a283ade97\");\n",
+       "    if (outputDiv.id !== \"altair-viz-be9820c1923e4b1a8a9166328af9c5a7\") {\n",
+       "      outputDiv = document.getElementById(\"altair-viz-be9820c1923e4b1a8a9166328af9c5a7\");\n",
        "    }\n",
        "    const paths = {\n",
        "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
        "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
-       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
+       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.17.0?noext\",\n",
        "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
        "    };\n",
        "\n",
@@ -876,12 +803,12 @@
        "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
        "    } else {\n",
        "      maybeLoadScript(\"vega\", \"5\")\n",
-       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
+       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.17.0\"))\n",
        "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
        "        .catch(showError)\n",
        "        .then(() => displayChart(vegaEmbed));\n",
        "    }\n",
-       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-14656ade87b5d77bf96f3e0cac0d9578.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean -10 and standard deviation 5\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
+       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-51adff2c72e9fac20dbe594018676cef.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean -10 and standard deviation 5\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.17.0.json\"}, {\"mode\": \"vega-lite\"});\n",
        "</script>"
       ],
       "text/plain": [
@@ -1681,10 +1608,38 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 30,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.collections.PathCollection at 0x1628911c0>"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Extended exercise\n",
+    "\n",
+    "possible_sums = [2,3,4,5,6,7,8,9,10,11,12]\n",
+    "pdf = [1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36]\n",
+    "cdf = [1/36, 3/36, 6/36, 10/36, 15/36, 21/36, 26/36, 30/36,33/36,35/36,1]\n",
+    "plt.scatter(possible_sums, cdf)\n"
+   ]
   },
   {
    "cell_type": "markdown",