diff --git a/normalverteilung.ipynb b/normalverteilung.ipynb index b60b28dfeac606d8fce05b61c74baa63818b3a7f..6857119368021cd58cdc3c1b73aee1b4e8cdc65f 100644 --- a/normalverteilung.ipynb +++ b/normalverteilung.ipynb @@ -21,7 +21,7 @@ "id": "af111971-55f2-4e9e-861c-4874ece317c1", "metadata": {}, "source": [ - "Betrachten wir eine Folge von Bernoulli-verteilten Zufallsvariablen $X_i$ mit gleichem Parameter $p$ und $S_n := \\sum_{i=1}^n X_i$ die Summe über die ersten $n$ davon, so wissen wir bereits, dass $S_n \\sim Bin(n,p)$, also dass diese Summe Binomialverteilt ist.\n", + "Betrachten wir eine Folge von Bernoulli-verteilten Zufallsvariablen $X_i$ mit gleichem Parameter $p$ und $S_n := \\sum_{i=1}^n X_i$ die Summe über die ersten $n$ davon, so wissen wir bereits, dass $S_n \\sim Bin(n,p)$, also dass diese Summe Binomialverteilt ist. Erinnerung: Das bedeutet, die pmf von $S_n$ ist $p(k) = \\binom{n}{k}p^k(1-p)^{n-k}$.\n", "\n", "Für die konkreten Werte $n=100,\\ p=0.4$ sieht ein Histogramm von $100000$ Samples etwa so aus:" ] @@ -38,14 +38,12 @@ "outputs": [ { "data": { - "image/png": "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", + "image/png": "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", "text/plain": [ - "<Figure size 432x288 with 1 Axes>" + "<Figure size 640x480 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -68,7 +66,7 @@ "id": "cf7b3ed2-f44a-4250-9cc4-ee10130f22cb", "metadata": {}, "source": [ - "Da diese Form für große Stichproben stets so aussieht, unabhängig von $p$ (probieren Sie das aus!), könnte man sich vorstellen, dass die Verteilung sich approximieren lässt mit Hilfe einer Funktion, die leichter zu berechnen ist als Binomialkoeffizienten.\n", + "Da diese Form für große Stichproben stets so aussieht, unabhängig von $p$ (probieren Sie das aus!), könnte man sich vorstellen, dass die Verteilung sich approximieren lässt mit Hilfe einer Funktion, die leichter zu berechnen ist als Binomialkoeffizienten $\\binom{n}{k} = \\frac{n!}{k!(n-k)!}$.\n", "\n", "Tatsächlich gibt es zur Approximation von Binomialkoeffizienten auch die *Stirling-Formel*\n", "\n", @@ -85,7 +83,7 @@ "metadata": {}, "source": [ "$$\n", - "P(S_n = k) \\sim\n", + "P(S_n = k) = \\binom{n}{k}p^k(1-p)^{n-k} \\sim\n", "\\frac{1}{\\sqrt{np(1-p)}} \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{x^2}{2}} \\quad \\text{ fuer } n \\to \\infty\n", "$$" ] @@ -177,14 +175,12 @@ "outputs": [ { "data": { - "image/png": "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", + "image/png": "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", "text/plain": [ - "<Figure size 432x288 with 1 Axes>" + "<Figure size 640x480 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -333,7 +329,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.11.2" } }, "nbformat": 4,