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tut4: Fix typos; Implement student corrections

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Andreas Tsouchlos 2025-12-19 04:23:53 +01:00
parent 088d448e50
commit d7725a0186
1 changed files with 8 additions and 8 deletions
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src/2025-12-19/presentation.tex
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@ -99,7 +99,7 @@
\pause\column{\kitthreecolumns}
\centering
\begin{itemize}
\item Verteilungsfunktion $F_X(x)$ einer stetiger ZV
\item Verteilungsfunktion $F_X(x)$ einer stetigen ZV
\begin{gather*}
F_X(x) = P(X \le x)
\end{gather*}
@ -107,7 +107,7 @@
\pause\column{\kitthreecolumns}
\centering
\begin{itemize}
\item Wahrscheinlichkeitsdichte $f_X(x)$ einer stetiger ZV
\item Wahrscheinlichkeitsdichte $f_X(x)$ einer stetigen ZV
\begin{gather*}
F_X(x) = \int_{-\infty}^{x} f_X(u) du
\end{gather*}
@ -154,7 +154,7 @@
\end{minipage}
\begin{minipage}{0.38\textwidth}
\begin{lightgrayhighlightbox}
Erinnerung
Erinnerung: Diskrete Zufallsvariablen
\begin{align*}
\text{\normalfont Erwartungswert: }& E(X) =
\sum_{n=1}^{\infty} x_n P_X(x) \\
@ -171,7 +171,7 @@
\begin{columns}[t]
\column{\kitthreecolumns}
\centering
\begin{greenblock}{Verteilungsfunktion (kontinuierlich)}
\begin{greenblock}{Verteilungsfunktion (stetige ZV)}
\vspace*{-6mm}
\begin{gather*}
F_X(x) = P(X \le x)\\[4mm]
@ -270,9 +270,9 @@
\end{align*}
\pause\begin{gather*}
\int_{-\infty}^{\infty} f_X(x) dx
= \int_{-\infty}^{\infty} C\cdot x e^{-ax^2} dx
= \frac{C}{-2a} \int_{-\infty}^{\infty} (-2ax) e^{-ax^2} dx \\
= \frac{C}{-2a} \int_{-\infty}^{\infty} (e^{-ax^2})' dx
= \int_{0}^{\infty} C\cdot x e^{-ax^2} dx
= \frac{C}{-2a} \int_{0}^{\infty} (-2ax) e^{-ax^2} dx \\
= \frac{C}{-2a} \int_{0}^{\infty} (e^{-ax^2})' dx
= \frac{C}{-2a} \mleft[ e^{-ax^2} \mright]_0^{\infty} \overset{!}{=} 1 \hspace{10mm} \Rightarrow C = 2a
\end{gather*}
\centering
@ -711,7 +711,7 @@
2 - 2\Phi\left(\frac{0{,}2}{\sigma'}\right) = 2{,}12\cdot 10^{-3} \\[2mm]
\Rightarrow \Phi\left(\frac{0{,}2}{\sigma'}\right) \approx 0{,}9989 \\[2mm]
\Rightarrow \sigma' \approx \frac{0{,}2}{\Phi^{-1}(0{,}9989)}
\approx \frac{0{,}2}{3{,}08} \approx 0{,}65
\approx \frac{0{,}2}{3{,}08} \approx 0{,}065
\end{gather*}
\end{columns}
\pause \vspace*{-5mm}\item Durch einen Produktionsfehler verschiebt sich der