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authorHeadAndToes <55713950+HeadAndToes@users.noreply.github.com>2022-07-19 16:42:27 +0200
committerGitHub <noreply@github.com>2022-07-19 16:42:27 +0200
commitc4fd6a857d14abdcc91ce84237f542561520d15a (patch)
tree8465f77faf415379e84bd112e67cc4d27113201d /vorlesungen/slides/dreieck/minmax.tex
parentKorrektur Feedback (diff)
parentmakefile fix (diff)
downloadSeminarSpezielleFunktionen-c4fd6a857d14abdcc91ce84237f542561520d15a.tar.gz
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Merge branch 'AndreasFMueller:master' into master
Diffstat (limited to 'vorlesungen/slides/dreieck/minmax.tex')
-rw-r--r--vorlesungen/slides/dreieck/minmax.tex22
1 files changed, 20 insertions, 2 deletions
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}