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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-05-20 20:24:26 +0200 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-05-20 20:24:26 +0200 |
commit | d3b772e811ac42cb912cce367b8e7bee07881084 (patch) | |
tree | 1dd80933a86f8d2cb98c6333d3093fbc2a951c1d /vorlesungen/slides/9/parrondo/spielb.tex | |
parent | add new slides (diff) | |
download | SeminarMatrizen-d3b772e811ac42cb912cce367b8e7bee07881084.tar.gz SeminarMatrizen-d3b772e811ac42cb912cce367b8e7bee07881084.zip |
add slides
Diffstat (limited to 'vorlesungen/slides/9/parrondo/spielb.tex')
-rw-r--r-- | vorlesungen/slides/9/parrondo/spielb.tex | 25 |
1 files changed, 21 insertions, 4 deletions
diff --git a/vorlesungen/slides/9/parrondo/spielb.tex b/vorlesungen/slides/9/parrondo/spielb.tex index 6ad512c..f65564f 100644 --- a/vorlesungen/slides/9/parrondo/spielb.tex +++ b/vorlesungen/slides/9/parrondo/spielb.tex @@ -15,6 +15,7 @@ Gewinn $\pm 1$, Wahrscheinlichkeit abhängig vom 3er-Rest des aktuellen Kapitals $K$: \begin{center} +\uncover<2->{% \begin{tikzpicture}[>=latex,thick] \coordinate (A0) at (90:2); \coordinate (A1) at (210:2); @@ -47,11 +48,12 @@ aktuellen Kapitals $K$: \node at (150:\R) {$\frac1{4}$}; \node at (270:\R) {$\frac14$}; -\end{tikzpicture} +\end{tikzpicture}} \end{center} \end{block} \end{column} \begin{column}{0.48\textwidth} +\uncover<3->{% \begin{block}{Markov-Kette $Y$} Übergangsmatrix \[ @@ -61,22 +63,37 @@ B=\begin{pmatrix} \frac{9}{10}&\frac34&0 \end{pmatrix} \] +\vspace{-10pt} + +\uncover<4->{% Gewinnmatrix: +\vspace{-2pt} \[ G=\begin{pmatrix*}[r] 0&-1&1\\ 1&0&-1\\ -1&1&0 \end{pmatrix*} -\] -\end{block} +\]} +\end{block}} +\vspace{-12pt} +\uncover<5->{% \begin{block}{Gewinnerwartung} \begin{align*} +&&&& E(Y) &= U^t(G\odot B)p +\\ +p&={\textstyle\frac13}U +&&\Rightarrow& +E(Y)&={\textstyle\frac1{15}} +\\ +\overline{p}&={\tiny\frac{1}{13}\begin{pmatrix}5\\2\\6\end{pmatrix}} +&&\Rightarrow& +E(Y)&=0 \end{align*} -\end{block} +\end{block}} \end{column} \end{columns} \end{frame} |