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| author | Patrik Müller <36931350+p1mueller@users.noreply.github.com> | 2022-05-31 16:31:34 +0200 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2022-05-31 16:31:34 +0200 |
| commit | 37d938d0d5803ef65de1cb3e780781e140002698 (patch) | |
| tree | 14ed570000f0870be8a13261a81dcc0228e1c62e /vorlesungen/slides/dreieck/minmax.tex | |
| parent | Add rule of thumb, analyse integrand, correct mistake in integration SLP<->LP (diff) | |
| parent | fix participant lists (diff) | |
| download | SeminarSpezielleFunktionen-37d938d0d5803ef65de1cb3e780781e140002698.tar.gz SeminarSpezielleFunktionen-37d938d0d5803ef65de1cb3e780781e140002698.zip | |
Merge branch 'AndreasFMueller:master' into master
Diffstat (limited to 'vorlesungen/slides/dreieck/minmax.tex')
| -rw-r--r-- | vorlesungen/slides/dreieck/minmax.tex | 22 |
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} |