From 293c84dfc5ec8511af15d699ccc9140c8b9b3679 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 9 Mar 2022 11:22:17 +0100 Subject: add sample slides and presentations --- vorlesungen/slides/dreieck/minmax.tex | 65 +++++++++++++++++++++++++++++++++++ 1 file changed, 65 insertions(+) create mode 100644 vorlesungen/slides/dreieck/minmax.tex (limited to 'vorlesungen/slides/dreieck/minmax.tex') diff --git a/vorlesungen/slides/dreieck/minmax.tex b/vorlesungen/slides/dreieck/minmax.tex new file mode 100644 index 0000000..9ef8d1a --- /dev/null +++ b/vorlesungen/slides/dreieck/minmax.tex @@ -0,0 +1,65 @@ +% +% minmax.tex -- Minimum und Maximum +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Minimum und Maximum} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Maximum} +Verteilungsfunktion von +\[ +Z=\operatorname{max}(X_1,\dots,X_n) +\] +\begin{align*} +F_Z(x) +&= +P(Z\le x) +\\ +&= +P(X_1\le x\wedge\dots\wedge X_n\le x) +\\ +&= +P(X_1\le x)\cdot \ldots\cdot P(X_n\le x) +\\ +&= +F_X(x)^n +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Minimum} +Verteilungsfunktion von +\[ +Z=\operatorname{min}(X_1,\dots,X_n) +\] +\begin{align*} +F_Z(x) +&= +P(Z\le x) +\\ +&=P(\overline{ +X_1\le x\wedge\dots\wedge X_n \le x +}) +\\ +&= +1-P( +X_1> x\wedge\dots\wedge X_n > x +) +\\ +&= +1-(P(X_1>x)\cdot\ldots\cdot P(X_n>x)) +\\ +&= +1-(1-F_X(x))^n +\end{align*} +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup -- cgit v1.2.1 From c49717a11a534d1621f819c7a114924047046a04 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 30 May 2022 11:38:12 +0200 Subject: new slides --- vorlesungen/slides/dreieck/minmax.tex | 22 ++++++++++++++++++++-- 1 file changed, 20 insertions(+), 2 deletions(-) (limited to 'vorlesungen/slides/dreieck/minmax.tex') diff --git a/vorlesungen/slides/dreieck/minmax.tex b/vorlesungen/slides/dreieck/minmax.tex index 9ef8d1a..ff3a231 100644 --- a/vorlesungen/slides/dreieck/minmax.tex +++ b/vorlesungen/slides/dreieck/minmax.tex @@ -17,48 +17,66 @@ Verteilungsfunktion von Z=\operatorname{max}(X_1,\dots,X_n) \] \begin{align*} +\uncover<3->{ F_Z(x) &= -P(Z\le x) +P(Z\le x)} \\ +\uncover<4->{ &= P(X_1\le x\wedge\dots\wedge X_n\le x) +} \\ +\uncover<5->{ &= P(X_1\le x)\cdot \ldots\cdot P(X_n\le x) +} \\ +\uncover<6->{ &= F_X(x)^n +} \end{align*} \end{block} \end{column} \begin{column}{0.48\textwidth} +\uncover<2->{% \begin{block}{Minimum} Verteilungsfunktion von \[ Z=\operatorname{min}(X_1,\dots,X_n) \] \begin{align*} +\uncover<7->{ F_Z(x) &= P(Z\le x) +} \\ +\uncover<8->{ &=P(\overline{ X_1\le x\wedge\dots\wedge X_n \le x }) +} \\ +\uncover<9->{ &= 1-P( X_1> x\wedge\dots\wedge X_n > x ) +} \\ +\uncover<10->{ &= 1-(P(X_1>x)\cdot\ldots\cdot P(X_n>x)) +} \\ +\uncover<11->{ &= 1-(1-F_X(x))^n +} \end{align*} -\end{block} +\end{block}} \end{column} \end{columns} \end{frame} -- cgit v1.2.1