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+\paragraph{c)} Berechnen Sie $P(X >\frac{\pi}{2})$. \textbf{(2 Punkte)}\\ +\begin{tabular}{| p{17cm} |} + \hline + \\\hline +\end{tabular} -\paragraph{d)} Berechnen Sie $E X$. \textbf{(2 Punkte)} -\begin{center} - \framebox(450,100){} -\end{center} +\paragraph{d)} Berechnen Sie $E X$. \textbf{(2 Punkte)}\\ +\begin{tabular}{| p{17cm} |} + \hline + \\\hline +\end{tabular} -\paragraph{e)} Begründen Sie, dass hier die Markoff-Ungleichung angewendet werden kann und verwenden Sie sie, um $P(X >\frac{\pi}{2})$ abzuschätzen. Wie erklären Sie den Unterschied zu c)? \textbf{(3 Punkte)} -\begin{center} - \framebox(450,100){} -\end{center} +\paragraph{e)} Begründen Sie, dass hier die Markoff-Ungleichung angewendet werden kann und verwenden Sie sie, um $P(X >\frac{\pi}{2})$ abzuschätzen. Wie erklären Sie den Unterschied zu c)? \textbf{(3 Punkte)}\\ +\begin{tabular}{| p{17cm} |} + \hline + \\\hline +\end{tabular} \section{Aufgabe 8: Deskriptive Statistik} Aus einer Charge von Fäden werden 5 Stück entnommen, um sie auf Reißfestigkeit zu testen. Notiert werden die erreichten Dehnungslängen $L_i,i= 1,...,5$ in cm zum Zeitpunkt des Reißens. Die Ergebnisse lauten: \begin{tabular}{c | c | c | c | c} - $L_1$ & $L_2$ & $L_3$ & $L_4$ & $L_5$ \\ - 4 & 11 & 1 & 6 & 3 + $L_1$ & $L_2$ & $L_3$ & $L_4$ & $L_5$ \\ + 4 & 11 & 1 & 6 & 3 \end{tabular} -\paragraph{a)} Befinden sich diese Daten auf einer Verhältnisskala? \textbf{(1 Punkt)} -\begin{center} - \framebox(450,100){} -\end{center} +\paragraph{a)} Befinden sich diese Daten auf einer Verhältnisskala? \textbf{(1 Punkt)}\\ +\begin{tabular}{| p{17cm} |} + \hline + \\\hline +\end{tabular} -\paragraph{b)} Skizzieren Sie die empirische Verteilungsfunktion zu diesem Datensatz. \textbf{(1 Punkt)} -\begin{center} - \framebox(450,100){} -\end{center} +\paragraph{b)} Skizzieren Sie die empirische Verteilungsfunktion zu diesem Datensatz. \textbf{(1 Punkt)}\\ +\begin{tabular}{| p{17cm} |} + \hline + \\\hline +\end{tabular} -\paragraph{c)} Bestimmen Sie den Mittelwert, den Median, die Quartile und den Interquartilsabstand der Daten. Wie erklärt sich der Unterschied zwischen Median und Mittelwert? \textbf{(4 Punkte)} -\begin{center} - \framebox(450,100){} -\end{center} +\paragraph{c)} Bestimmen Sie den Mittelwert, den Median, die Quartile und den Interquartilsabstand der Daten. Wie erklärt sich der Unterschied zwischen Median und Mittelwert? \textbf{(4 Punkte)}\\ +\begin{tabular}{| p{17cm} |} + \hline + \\\hline +\end{tabular} -\paragraph{d)} Skizzieren Sie einen Boxplot zu diesem Datensatz. \textbf{(3 Punkte)} -\begin{center} - \framebox(450,100){} -\end{center} +\paragraph{d)} Skizzieren Sie einen Boxplot zu diesem Datensatz. \textbf{(3 Punkte)}\\ +\begin{tabular}{| p{17cm} |} + \hline + \\\hline +\end{tabular}