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authorLordMcFungus <mceagle117@gmail.com>2022-07-22 21:28:45 +0200
committerGitHub <noreply@github.com>2022-07-22 21:28:45 +0200
commit23f17598c1742c70f442b94044a20aa821022c5a (patch)
treea945540ee6a4e86b37df2f01e3a91584b4797c4f /vorlesungen/slides/dreieck/minmax.tex
parentMerge pull request #2 from AndreasFMueller/master (diff)
parentMerge pull request #25 from JODBaer/master (diff)
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Merge pull request #3 from AndreasFMueller/master
update
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}