49 lines
No EOL
2.2 KiB
TeX
49 lines
No EOL
2.2 KiB
TeX
\documentclass[14pt]{extarticle}
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\renewcommand{\tablename}{Ergänzung}
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\title{doofes mathe ding}
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\usepackage{rotating}
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\usepackage{float}
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\renewcommand{\arraystretch}{2.5}
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\pagenumbering{gobble}
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\usepackage[table]{xcolor}
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\usepackage[left=1cm, right=1cm, top=1cm, bottom=1cm]{geometry}
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\begin{document}
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\begin{sidewaystable}
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\centering
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\rowcolors{2}{gray!25}{white}
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\begin{tabular}{|l|l|l|l|l|}
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\hline
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\rowcolor{gray!50}
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Stichprobenfunktion & Bezeichnung & Erwartungswert & Varianz & Verteilung \\
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\hline
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$\sum^{n}_{i = 1} X_i$ & Merkmalsumme & $n \cdot \mu$ & $n \cdot \sigma^2$ & $N(n \mu, \sigma \sqrt{n})$ \\
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\hline
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$\overline{X} = \frac{1}{n} \sum_{i=1}^{n} X_i$ & Stichprobenmittel & $\mu$ & $\frac{\sigma ^2}{n}$ & $N(\mu), \frac{\sigma}{\sqrt{n}}$ \\
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\hline
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$\frac{\overline{X} - \mu}{\sigma} \cdot \sqrt{n}$ & Gauß-Statistik & 0 & 1 & $N(0,1)$ \\
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\hline
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$\frac{1}{n} \sum_{i=1}^{n}(X_i - \mu)^2$ & mittlere quadratische Abweichung bzgl. $\mu$ & $\sigma ^2$ & $2\sigma ^2$ & \quad \\
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\hline
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$\frac{1}{n} \cdot \sum^{n}_{i=1} (X_i - \overline{X})^2$ & mittlere quadratische Abweichung & $\frac{n -1}{n} \cdot \sigma^2$ & $2 \cdot \frac{n-1}{n} \cdot \sigma^2$ & \\
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\hline
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$S^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i-\overline{X})^2$ & Stichprobenvarianz & $\sigma ^2$ & $2 \sigma ^2$ & \\
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\hline
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$S = \sqrt{S^2}$ & Stichproben-Standartabweichung & $\leq \sigma$ & & \\
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\hline
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$\frac{\overline{X} - \mu}{S} \cdot \sqrt{n}$ & t-Statistik & 0 & $\frac{n}{n -2}$ & \\
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\hline
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$\frac{1}{\sigma ^2} \sum_{i=1}{n} (X_i - \mu)^2$ & & & & $\chi ^2(n)$ \\
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\hline
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$\frac{1}{\sigma ^2} \sum_{i=1}{n} (X_i - \overline{X})^2 = \frac{n-1}{\sigma ^2} \cdot S^2$ & & & & $\chi^2 (n-1)$ \\
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\hline
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$\frac{\overline{X} - \mu}{S}$ & & & &$Z(n-1)$ \\
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\hline
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\end{tabular}
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\caption{Verteilung wichtiger Stichprobenfunktionen (wilde Likelihood Dinge)}
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\label{tab:Likelihood}
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\end{sidewaystable}
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\end{document} |