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Aufgabe 31 UE Wahrscheinlichkeitstheorie
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"# Aufgabe 31" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Das Ziegenproblem wurde als ein Beispiel für bedingte Wahrscheinlichkeit in der Vorlesung erwähnt. (Siehe z.B. https://de.wikipedia.org/wiki/Ziegenproblem oder das Buch *Das Ziegenproblem: Denken in Wahrscheinlichkeiten von Gero von Randow* für eine weitere Erklärung.) Führen Sie ein Experiment mit 30 Versuchsreihen durch und stellen Sie Ihre Erfahrungen mit zwei Stabdiagrammen grafisch dar!" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import random\n", | |
"import plotly.offline as pl # Für die Barcharts\n", | |
"import plotly.graph_objs as go # Für die Barcharts" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"N=1000" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def spiel(wechseln):\n", | |
" hinter_türen = list('zza') # z=Ziege, a=Auto\n", | |
" random.shuffle(hinter_türen)\n", | |
" spieler_tür=random.randint(0,2) # Spieler wählt zufällig eine Tür\n", | |
" if not wechseln:\n", | |
" return hinter_türen[spieler_tür]\n", | |
" if hinter_türen[spieler_tür]=='a':\n", | |
" return 'z'\n", | |
" return 'a'" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def simulate(wechseln, N=N):\n", | |
" return (''.join(spiel(wechseln) for _ in range(N))).count('a')/N\n", | |
" " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": [ | |
"<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>" | |
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"<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>" | |
] | |
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"metadata": {}, | |
"output_type": "display_data" | |
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"data": { | |
"application/vnd.plotly.v1+json": { | |
"config": { | |
"linkText": "Export to plot.ly", | |
"plotlyServerURL": "https://plot.ly", | |
"showLink": false | |
}, | |
"data": [ | |
{ | |
"type": "bar", | |
"uid": "6651a7fc-2b09-421a-b18a-14593ee7e360", | |
"x": [ | |
"Wechseln", | |
"Bleiben" | |
], | |
"y": [ | |
0.661, | |
0.311 | |
] | |
} | |
], | |
"layout": { | |
"barmode": "relative", | |
"title": { | |
"text": "Relativer Anteil an Spielen in denen das Auto gewonnen wird. N=1000" | |
}, | |
"xaxis": { | |
"title": { | |
"text": "Strategie" | |
} | |
}, | |
"yaxis": { | |
"title": { | |
"text": "Relative Häufigkeit" | |
} | |
} | |
} | |
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"<div id=\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";\n", | |
"if (document.getElementById(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\")) {\n", | |
" Plotly.newPlot(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\", [{\"x\": [\"Wechseln\", \"Bleiben\"], \"y\": [0.661, 0.311], \"type\": \"bar\", \"uid\": \"6651a7fc-2b09-421a-b18a-14593ee7e360\"}], {\"barmode\": \"relative\", \"title\": {\"text\": \"Relativer Anteil an Spielen in denen das Auto gewonnen wird. N=1000\"}, \"xaxis\": {\"title\": {\"text\": \"Strategie\"}}, \"yaxis\": {\"title\": {\"text\": \"Relative H\\u00e4ufigkeit\"}}}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"plotlyServerURL\": \"https://plot.ly\"}); \n", | |
"}\n", | |
"});</script><script type=\"text/javascript\">window.addEventListener(\"resize\", function(){if (document.getElementById(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\")) {window._Plotly.Plots.resize(document.getElementById(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\"));};})</script>" | |
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"<div id=\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";\n", | |
"if (document.getElementById(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\")) {\n", | |
" Plotly.newPlot(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\", [{\"x\": [\"Wechseln\", \"Bleiben\"], \"y\": [0.661, 0.311], \"type\": \"bar\", \"uid\": \"6651a7fc-2b09-421a-b18a-14593ee7e360\"}], {\"barmode\": \"relative\", \"title\": {\"text\": \"Relativer Anteil an Spielen in denen das Auto gewonnen wird. N=1000\"}, \"xaxis\": {\"title\": {\"text\": \"Strategie\"}}, \"yaxis\": {\"title\": {\"text\": \"Relative H\\u00e4ufigkeit\"}}}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"plotlyServerURL\": \"https://plot.ly\"}); \n", | |
"}\n", | |
"});</script><script type=\"text/javascript\">window.addEventListener(\"resize\", function(){if (document.getElementById(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\")) {window._Plotly.Plots.resize(document.getElementById(\"2036a17f-4a60-4b9b-8ea6-ca485aef90fe\"));};})</script>" | |
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} | |
], | |
"source": [ | |
"pl.init_notebook_mode(connected=True)\n", | |
"layout = {\n", | |
" 'xaxis': {'title': 'Strategie'},\n", | |
" 'yaxis': {'title': 'Relative Häufigkeit'},\n", | |
" 'barmode': 'relative',\n", | |
" 'title': 'Relativer Anteil an Spielen in denen das Auto gewonnen wird. N=%d'%N\n", | |
"}\n", | |
"data = [go.Bar(\n", | |
" x = ['Wechseln', 'Bleiben'],\n", | |
" y = [simulate(True), simulate(False)]\n", | |
" )]\n", | |
"fig = go.FigureWidget(data, layout)\n", | |
"pl.iplot(fig)" | |
] | |
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"nbformat": 4, | |
"nbformat_minor": 2 | |
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