From 293c84dfc5ec8511af15d699ccc9140c8b9b3679 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
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?= <andreas.mueller@ost.ch>
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