aboutsummaryrefslogtreecommitdiffstats
path: root/vorlesungen/slides/dreieck/minmax.tex
diff options
context:
space:
mode:
authorSamuel Niederer <43746162+samnied@users.noreply.github.com>2022-07-24 12:17:00 +0200
committerGitHub <noreply@github.com>2022-07-24 12:17:00 +0200
commitefe7c35759afb5cbae3c1683873c5159be0be09f (patch)
tree84f2e8510132352f9943bddc577ccf32cd46f2dc /vorlesungen/slides/dreieck/minmax.tex
parentadd current work (diff)
parentMerge pull request #26 from p1mueller/master (diff)
downloadSeminarSpezielleFunktionen-efe7c35759afb5cbae3c1683873c5159be0be09f.tar.gz
SeminarSpezielleFunktionen-efe7c35759afb5cbae3c1683873c5159be0be09f.zip
Merge branch 'AndreasFMueller:master' into master
Diffstat (limited to 'vorlesungen/slides/dreieck/minmax.tex')
-rw-r--r--vorlesungen/slides/dreieck/minmax.tex83
1 files changed, 83 insertions, 0 deletions
diff --git a/vorlesungen/slides/dreieck/minmax.tex b/vorlesungen/slides/dreieck/minmax.tex
new file mode 100644
index 0000000..ff3a231
--- /dev/null
+++ b/vorlesungen/slides/dreieck/minmax.tex
@@ -0,0 +1,83 @@
+%
+% 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*}
+\uncover<3->{
+F_Z(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{column}
+\end{columns}
+\end{frame}
+\egroup