{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "757e8eab-8ae6-4d3c-9159-276476a79e7a",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "---------------------------------\n",
      "Working on the host: Joachims-MacBook-Pro.local\n",
      "\n",
      "---------------------------------\n",
      "Python version: 3.10.2 | packaged by conda-forge | (main, Feb  1 2022, 19:30:18) [Clang 11.1.0 ]\n",
      "\n",
      "---------------------------------\n",
      "Python interpreter: /opt/miniconda3/envs/srh/bin/python\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Load the \"autoreload\" extension\n",
    "%load_ext autoreload\n",
    "# always reload modules\n",
    "%autoreload 2\n",
    "# black formatter for jupyter notebooks\n",
    "#%load_ext nb_black\n",
    "# black formatter for jupyter lab\n",
    "%load_ext lab_black\n",
    "\n",
    "%run ../../src/notebook_env.py"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81643a74-cd4c-4740-a14c-889646bffb5b",
   "metadata": {},
   "source": [
    "# Diskrete Zufallsvariablen und ihre Wahrscheinlichkeitsverteilungen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8454e2d8-3177-48e3-b37a-58959b4bfb66",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6aa8612e-b3a3-4bb1-ad5f-8cc1b02ada5f",
   "metadata": {},
   "source": [
    "Eine <a href=\"https://de.wikipedia.org/wiki/Zufallsvariable\">Zufallsvariable</a> ist eine Variable, deren Wert vom Zufall abhängt; dementsprechend ist ihr Wert mit einer Wahrscheinlichkeit verbunden. Generell sind Zufallsvariablen Zuordnungsvorschriften die möglichen Ergebnissen eines Zufallsexperiments einen Zahlenwert zuordnen. Eine **diskrete Zufallsvariable** weist den möglichen Ergebnissen diskrete, also abzählbare Werte zu. Eine **Wahrscheinlichkeitsverteilung** ist eine Auflistung der möglichen Werte und der entsprechenden Wahrscheinlichkeiten einer diskreten Zufallsvariablen, die häufig durch eine Formel dargestellt wird."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "987e8cf6-75c5-4b9e-b4e9-bfa7204d0a58",
   "metadata": {},
   "source": [
    "Ein Diagramm der Wahrscheinlichkeitsverteilung, das die Wahrscheinlichkeit jedes Wertes, dargestellt durch einen vertikalen Balken, dessen Höhe der Wahrscheinlichkeit entspricht, und die möglichen Werte einer diskreten Zufallsvariablen auf der horizontalen Achse anzeigt, wird **Wahrscheinlichkeitshistogramm** genannt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3684eb64-3628-497d-a71b-5779a95c5de2",
   "metadata": {},
   "source": [
    "Die **Summe der Wahrscheinlichkeiten einer diskreten Zufallsvariablen** für eine beliebige diskrete Zufallsvariable $X$ wird geschrieben als"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10d695f5-483b-45e2-9e1c-fdc7bb0689db",
   "metadata": {},
   "source": [
    "$$\\sum_{i=1}^{N}P(X = x_i) = 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfbe6720-8b55-4972-ac58-0a4084e846b4",
   "metadata": {},
   "source": [
    "Bei einer großen Anzahl an voneinander unabhängigen Beobachtungen einer Zufallsvariablen $X$ wird das Wahrscheinlichkeitshistogramm eine Annäherung an die Wahrscheinlichkeitsverteilung für $X$ darstellen ({cite:p}`fahrmeirstatistik` s.209-250)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2f69874-4ab4-4f39-a8fd-c6da9799d41d",
   "metadata": {},
   "source": [
    "## Diskrete Zufallsvariablen - ein Beispiel"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "640d4fc1-62a8-4d69-a988-1af25ed21a74",
   "metadata": {},
   "source": [
    "Lassen Sie uns das Konzept der **diskreten Zufallsvariablen** anhand eines Beispiels erläutern."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "957019b7-53f7-4251-9a1f-efdef3552c5d",
   "metadata": {},
   "source": [
    "Unsere zu untersuchende Population besteht aus allen Studierenden, allen Dozenten und allen Verwaltungsmitarbeitern der <a href=\"https://www.fu-berlin.de/\">FU Berlin</a>. Wir wählen zufällig eine dieser Personen aus und fragen sie nach der Anzahl ihrer Geschwister. Folglich ist die Antwort, die Anzahl der Geschwister einer zufällig ausgewählten Person, eine diskrete Zufallsvariable, bezeichnet als $X$. Der tatsächliche Wert (Anzahl der Geschwister) von $X$ hängt vom Zufall ab, aber wir können trotzdem alle Werte von $X$ auflisten, z.B. $0$ Geschwister, $1$ Geschwister, $2$ Geschwister, usw. Zur Vereinfachung beschränken wir die Anzahl der Geschwister in dieser Übung auf $5$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1b4677d-2bcb-4ed6-bb30-94ea3b8d51a2",
   "metadata": {},
   "source": [
    "Laut der <a href=\"https://www.fu-berlin.de/universitaet/profil/zahlen/index.html\">Website</a> der FU Berlin gibt es im WS 2021/2022 $33.000$ Studierende, $4.000$ Doktoranden, $379$ Professoren und $4.660$ Mitarbeiter an der FU Berlin (bitte beachten Sie, dass sich die tatsächlichen Zahlen im Laufe der Zeit ändern können)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17e2bb61-58d4-4e90-a424-06fbc5ea0e33",
   "metadata": {},
   "source": [
    "Da wir keine Vorstellung von der damit verbundenen Wahrscheinlichkeit für eine bestimmte Anzahl von Geschwistern haben, starten wir einige Experimente:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00f62fde-569f-4a3e-8a48-6d6d4b984d90",
   "metadata": {},
   "source": [
    "Wir wählen **eine** zufällig ausgewählte Person aus und fragen nach der Anzahl der Geschwister."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53388a79-5d04-4025-a672-fda94213a056",
   "metadata": {},
   "source": [
    "Die Antwort lautet: $0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a5f04c4-4d3c-45b0-8e71-3b9582c9df2e",
   "metadata": {},
   "source": [
    "Wir wählen **zehn** zufällig ausgewählte Personen aus und befragen sie zu ihren Geschwistern."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8349b5f4-ec25-4049-bf32-78d5d834c29b",
   "metadata": {},
   "source": [
    "Die Antworten lauten: $4,0,2,0,2,2,1,2,0,3$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04610af3-445a-4fd8-b2f2-a32a51d5e927",
   "metadata": {},
   "source": [
    "Wir wählen *hundert* Personen aus und fragen nach Geschwistern."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e84326ab-4f27-4034-9803-967821ad7e43",
   "metadata": {},
   "source": [
    "Die Antworten lauten: $2, 0, 1, 2, 2, 0, 0, 0, 1, 3, 1, 2, 1, 0, 2, 0, 0, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 0, 1, 1, 2, 4, 0, 3, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 0, 2, 0, 1, 0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 0, 2, 2, 4, 1, 2, 1, 1, 1, 1, 1, 0, 2, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28ce176a-817c-4477-9f91-3b8f2d73a3bb",
   "metadata": {},
   "source": [
    "Sie sehen, die Form der Notation wird ziemlich schnell unübersichtlich, wenn wir die Anzahl der abgefragten Individuen erhöhen. Wir beschließen also, die **Häufigkeit** und die entsprechende **relative Häufigkeit** der Werte für die Klassen $0$, $1$, $2$, $3$, $4$, $5$ (um es deutlich zu sagen: die letzte Klasse entspricht $5$ oder mehr Geschwistern) zu notieren und das Experiment in Form einer schön formatierten Tabelle zu präsentieren."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bce004a-0b57-45df-b7ff-804b001a13ae",
   "metadata": {},
   "source": [
    "Wir wählen $1.000$ Personen aus und befragen sie zu ihren Geschwistern."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a529ca5",
   "metadata": {},
   "source": [
    "|Geschwister ($x$)|Absolute Häufigkeit($f$)|Relative Häufigkeit|\n",
    "|:---:|:---:|:---:|\n",
    "|0|205|0,205|\n",
    "|1|419|0,419|\n",
    "|2|280|0,28|\n",
    "|3|65|0,065|\n",
    "|4|29|0,029|\n",
    "|5|2|0,002|\n",
    "| |1000|1|"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd18badf-9dff-439e-8832-97e006460d4e",
   "metadata": {},
   "source": [
    "Nachdem wir alle möglichen Werte aufgelistet und die entsprechenden relativen Häufigkeiten berechnet haben, kennen wir immer noch nicht genau die Wahrscheinlichkeiten der diskreten Zufallsvariablen $X$ für die gesamte Population von $40.961$ Personen, die der FU Berlin zugeordnet sind. Nach Gesprächen mit $1.000$ zufällig ausgewählten Personen sind wir jedoch recht zuversichtlich, dass eine so große Anzahl von Interviews - verglichen mit der Anzahl der Gesamtpopulation $(40.961)$ - uns eine gute Annäherung an die Wahrscheinlichkeiten der diskreten Zufallsvariablen $X$ (Anzahl der Geschwister) für die Gesamtpopulation liefern wird."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62efda73-1017-46b9-a226-7683b01f3e14",
   "metadata": {},
   "source": [
    "Im nächsten Schritt zeichnen wir ein **Wahrscheinlichkeitshistogramm** (der Stichprobe), das die möglichen Werte einer diskreten Zufallsvariablen $X$ auf der horizontalen Achse und die Anteile dieser Werte auf der vertikalen Achse darstellt. Ein Verhältnishistogramm kann auch als Annäherung an die Wahrscheinlichkeitsverteilung dienen. Bitte beachten Sie, dass sowohl die **Summe der Wahrscheinlichkeiten** als auch die **Summe der Anteile** jeder diskreten Zufallsvariablen gleich $1$ ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "930b6e4d-df0f-4c52-ac16-02c85a3147d0",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Wahrscheinlichkeit')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Erzeuge Dataframe df\n",
    "p = [0.205, 0.419, 0.28, 0.065, 0.029, 0.002]\n",
    "x = [0, 1, 2, 3, 4, 5]\n",
    "\n",
    "# Säulendiagramm\n",
    "fig, ax = plt.subplots()\n",
    "ax.bar(\n",
    "    x,\n",
    "    p,\n",
    "    width=1.0,\n",
    "    edgecolor=\"k\",\n",
    ")\n",
    "\n",
    "# annotate\n",
    "ax.bar_label(ax.containers[0], label_type=\"edge\", size=12)\n",
    "ax.set_title(\n",
    "    \"Wahrscheinlichkeithistogramm der Zufallsvariablen X, die Anzahl der Geschwister zufällig \\n ausgewählter Einzelpersonen der FU Berlin\"\n",
    ")\n",
    "ax.set_xlabel(\"Anzahl Geschwister\")\n",
    "ax.set_ylabel(\"Wahrscheinlichkeit\", color=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b077478-14cf-4a8d-a670-335f488bc837",
   "metadata": {},
   "source": [
    "Bei vielen Anwendungen im wirklichen Leben kennen wir die Wahrscheinlichkeitsverteilung der Grundgesamtheit nicht - **und werden sie auch nie kennen**. Das liegt vor allem daran, dass in vielen Anwendungen die Grundgesamtheit viel zu groß ist oder es keine Möglichkeit gibt, zuverlässige Daten zu erhalten, oder wir weder das Geld noch die Zeit für eine umfassende Datenerhebung haben. Erhöht man jedoch die Anzahl der unabhängigen Beobachtungen einer Zufallsvariablen $X$, so nähert sich das Wahrscheinlichkeitshistogramm der Stichprobe immer mehr dem Wahrscheinlichkeitshistogramm der Grundgesamtheit an. Um diese Behauptung zu beweisen, vergrößern wir unser Experiment:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "515a636e-a389-4bbe-8c92-913cb7143516",
   "metadata": {},
   "source": [
    "Wir wählen nacheinander $10$, $100$ und $1.000$ zufällig Personen aus, die mit der FU Berlin verbunden sind, und befragen sie nach der Anzahl der Geschwister. Wir werden jedes unserer drei Experimente aufzeichnen und schließlich mit der tatsächlichen/realen Wahrscheinlichkeitsverteilung vergleichen (Bitte beachten Sie, dass dieses Beispiel ein Übungsbeispiel ist und nicht die reale Anzahl der Geschwister in der Population der Personen an der FU Berlin darstellt; daher *kennen* die Dozenten des vorliegenden Skripts die Wahrscheinlichkeitsverteilung der Grundgesamtheit ;-))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "52e29a13-b4c9-44be-85ed-d72e702ecc31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1008x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_prob_experiment = (0.2, 0.425, 0.275, 0.07, 0.025, 0.005)\n",
    "\n",
    "trialsize = [10, 100, 1000]\n",
    "siblings = [0, 1, 2, 3, 4, 5]\n",
    "np.random.seed(1)\n",
    "fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(14, 8))\n",
    "ax = np.ravel(ax)\n",
    "for e, n in enumerate(trialsize):\n",
    "    trial = np.random.choice(\n",
    "        range(len(_prob_experiment)), size=n, replace=True, p=_prob_experiment\n",
    "    )\n",
    "    unique_elements, counts_elements = np.unique(trial, return_counts=True)\n",
    "    counts = dict(zip(unique_elements, counts_elements / n))\n",
    "    df = pd.DataFrame.from_dict(counts, orient=\"index\", columns=[\"frequency\"])\n",
    "    df = df.reindex(siblings).fillna(0)\n",
    "    ax[e].bar(\n",
    "        df.index,\n",
    "        df.frequency,\n",
    "        width=1.0,\n",
    "        edgecolor=\"k\",\n",
    "    )\n",
    "    ax[e].bar_label(ax[e].containers[0], label_type=\"edge\", size=14)\n",
    "    ax[e].set_title(f\"Häufigkeitsverteilung (n={n})\")\n",
    "\n",
    "ax[3].bar(\n",
    "    siblings,\n",
    "    _prob_experiment,\n",
    "    width=1.0,\n",
    "    edgecolor=\"k\",\n",
    ")\n",
    "ax[3].bar_label(ax[3].containers[0], label_type=\"edge\", size=14)\n",
    "ax[3].set_title(f\"Die tatsächliche (unbekannte) Häufigkeitsverteilung\")\n",
    "\n",
    "for _ax in ax:\n",
    "    _ax.set_ylim(0, 0.6)\n",
    "    _ax.set_xlabel(\"Anzahl Geschwister\")\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d908fe28-92b9-4a34-8ad9-d44985ae1711",
   "metadata": {},
   "source": [
    "Die Diagramme bestätigen unsere Hypothese, dass sich das Histogramm der Stichprobe mit zunehmender Anzahl der Beobachtungen immer mehr dem Häufigkeitsverteilung der Grundgesamtheit annähert."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8082e014-e9aa-42bd-aaeb-d738833630bc",
   "metadata": {},
   "source": [
    "## Der Mittelwert und die Standardabweichung einer diskreten Zufallsvariablen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39e6d6c2-86e8-4e49-bf37-a9de16c71c6b",
   "metadata": {},
   "source": [
    "### Mittelwert einer diskreten Zufallsvariable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee5d33b1-d26d-4c07-9746-f13995f80ad9",
   "metadata": {},
   "source": [
    "Der Mittelwert einer **diskreten Zufallsvariablen** $X$ wird mit $\\mu_X$ oder, wenn keine Verwechslung auftreten soll, einfach mit $\\mu$ bezeichnet. Die Begriffe **Erwartungswert**, $E(X)$ und **Erwartung** werden üblicherweise anstelle des Begriffs Mittelwert verwendet."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef30d407-8f90-4794-9995-9572a50e1265",
   "metadata": {},
   "source": [
    "$$E(X) = \\sum_{i=1}^{N}x_iP(X=x_i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5197d998-9ab6-4293-b22e-a9ded23dc6eb",
   "metadata": {},
   "source": [
    "Bei einer großen Anzahl unabhängiger Beobachtungen einer Zufallsvariablen $X$ nähert sich $E(X)$ dieser Beobachtungen - der Stichprobe - dem Mittelwert $\\mu$ der Grundgesamtheit an. Je größer die Zahl der Beobachtungen ist, desto näher liegt $E(X)$ an $\\mu$ ({cite:p}`fahrmeirstatistik` s.226)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bcae2d0-542b-4239-887c-e4d2ab431520",
   "metadata": {},
   "source": [
    "Erinnern wir uns an unser Experiment aus dem vorherigen Abschnitt, als wir $1.000$ Personen ausgewählt und nach der Anzahl der Geschwister gefragt haben. Werfen wir noch einmal einen Blick auf die Tabelle, die das Experiment zusammenfasst"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebb75c1f-aacb-4b06-b90a-3b68cbae3d04",
   "metadata": {},
   "source": [
    "|Geschwister ($x$)|Absolute Häufigkeit($f$)|Relative Häufigkeit|\n",
    "|:---:|:---:|:---:|\n",
    "|0|205|0,205|\n",
    "|1|419|0,419|\n",
    "|2|280|0,28|\n",
    "|3|65|0,065|\n",
    "|4|29|0,029|\n",
    "|5|2|0,002|\n",
    "| |1000|1|"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0916f07c-43ce-4a46-a54f-bd0a1def7b08",
   "metadata": {},
   "source": [
    "Berechnen wir den Erwartungswert (Mittelwert) für dieses Experiment."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "576d3ae8-7d89-416d-a8c8-841e91370ea2",
   "metadata": {},
   "source": [
    "$E(X) = \\sum_{i=1}^{N}x_iP(X=x_i) $\n",
    "\n",
    "$ = 0 \\cdot P(X=0) + 1 \\cdot P(X=1)+ 2 \\cdot P(X=2) + 3 \\cdot P(X=3) +4 \\cdot P(X=4)+ 5 \\cdot P(X \\ge 5) $\n",
    "\n",
    "$ = 0 \\cdot 0,205 + 1 \\cdot 0,419 + 2 \\cdot 0,28+ 3 \\cdot 0,065  + 4 \\cdot 0,029  + 5 \\cdot 0,002  $\n",
    "\n",
    "$ = 1,3 $"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb84dec4-cb6f-4aac-99c6-14207b811f06",
   "metadata": {},
   "source": [
    "Der sich daraus ergebende Erwartungswert von $1,3$ liegt nahe am Mittelwert $\\mu$, den wir anhand der Wahrscheinlichkeiten der Grundgesamtheit berechnen (die realen Wahrscheinlichkeiten sind der unteren rechten Abbildung im vorherigen Abschnitt entnommen)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b4d7cee-740e-4658-b241-e887bc080ed5",
   "metadata": {},
   "source": [
    "$$\\mu = 1 \\cdot 0,2 + 2 \\cdot 0,425 +  3 \\cdot 0,275 + 4 \\cdot 0,07 + 5 \\cdot 0,025=1,31$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9730fa72-e43b-464f-8b4a-d64aca41d30f",
   "metadata": {},
   "source": [
    "### Übung"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72f4b885-bab6-42a5-bd73-94de98b43cd3",
   "metadata": {},
   "source": [
    "Betrachten wir einen fairen sechsseitigen Würfel. Wir können den **Erwartungswert** $E(X)$ leicht mit Python berechnen. Der Begriff \"fair\" bedeutet, dass jede Zufallsvariable $X=x_i,\\; x \\in 1,2,3,4,5,6$ mit gleicher Wahrscheinlichkeit auftritt. Daher ist $P(X=x_i)=\\frac{1}{6}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe2e7540-0e3a-4041-a34f-7b5452bcc6e0",
   "metadata": {},
   "source": [
    "$$E(X) = \\sum_{i=1}^{6}x_iP(X=x_i) = 1 \\cdot \\frac{1}{6} + 2 \\cdot \\frac{1}{6} +  3 \\cdot \\frac{1}{6} +  4 \\cdot \\frac{1}{6} + 5 \\cdot \\frac{1}{6} + 6 \\cdot \\frac{1}{6}= 3,5$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbb3ff72-8fdd-4d72-97e9-6973aa065acd",
   "metadata": {},
   "source": [
    "In Python schreiben wir den folgenden Code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bbc13bb0-e4d1-4a94-a092-90ce1684d4a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_die = 1 / 6\n",
    "die = pd.Series([1, 2, 3, 4, 5, 6])\n",
    "die = die * p_die\n",
    "sum(die)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4241423f-1a16-43a8-8bf1-4c058d2f290b",
   "metadata": {},
   "source": [
    "Was aber, wenn wir uns nicht sicher sind, ob die Würfel wirklich fair sind? Woher wissen wir, dass wir nicht betrogen werden? Oder anders ausgedrückt: Wie oft müssen wir würfeln, bevor wir mehr Vertrauen haben können?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d47bad66-4c82-403b-a8fc-d91ee1cef68e",
   "metadata": {},
   "source": [
    "Führen wir ein Berechnungsexperiment durch: Wir wissen aus den obigen Überlegungen, dass der Erwartungswert eines $6$-seitigen fairen Würfels $3,5$ ist. Wir führen ein Experiment durch, indem wir einen Würfel immer und immer wieder werfen. Wir speichern das Ergebnis und bevor wir erneut würfeln, berechnen wir den Durchschnitt aller bisherigen Würfelwürfe. Um dieses kleine Experiment durchzuführen, schreiben wir eine for-Schleife in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4100ecd7-52f7-4e49-9aac-99bad58b4cb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16a62cd30>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Setze random seed für Reproduzierbarkeit\n",
    "random.seed(10)\n",
    "wuerfel = []\n",
    "e_wert = []\n",
    "x = np.arange(0, 500, 1)\n",
    "# Simuliere Würfelwurf\n",
    "for i in range(500):\n",
    "    r = random.randint(1, 6)\n",
    "    wuerfel.append(r)\n",
    "    e_wert.append(np.mean(wuerfel))\n",
    "# Plotten\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, e_wert, lw=1)\n",
    "ax.axhline(y=3.5, color=\"C1\", linestyle=\"dashed\", label=\"Erwartungswert : 3,5\")\n",
    "ax.set_xlabel(\"Anzahl der Versuche\")\n",
    "ax.set_ylabel(\"Erwartungswert\")\n",
    "ax.set_ylim(1, 6.5)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c084ca7-ec82-4560-a958-c92ee56c428e",
   "metadata": {},
   "source": [
    "Das Diagramm zeigt, dass die Kurve nach anfänglichen Schwankungen schließlich abflacht und sich dem $E(X)$ von $3,5$ annähert."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf3913aa-135b-4e47-9654-44614f540248",
   "metadata": {},
   "source": [
    "### Standardabweichung einer diskreten Zufallsvariable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "362a3fd7-f5e8-492b-8fb5-6282caf9b5d8",
   "metadata": {},
   "source": [
    "Die Standardabweichung einer diskreten Zufallsvariablen $X$ wird mit $\\sigma_X$ oder, wenn keine Verwechslung auftreten soll, einfach mit $\\sigma$ bezeichnet. Sie ist definiert als"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8f84347-b329-4040-813a-215e63f856fe",
   "metadata": {},
   "source": [
    "$$\\sigma = \\sqrt{\\sum_{i=1}^{N}(x_i-\\mu)^2P(X=x_i)}$$"
   ]
  }
 ],
 "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": "3.10.2"
  },
  "vscode": {
   "interpreter": {
    "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}