From 80416f0ab893f2b80a01be4acc13bd03c7a03682 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 20 May 2021 10:09:26 +0200
Subject: add new slides

---
 vorlesungen/slides/9/parrondo/erwartung.tex | 76 +++++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)
 create mode 100644 vorlesungen/slides/9/parrondo/erwartung.tex

(limited to 'vorlesungen/slides/9/parrondo/erwartung.tex')

diff --git a/vorlesungen/slides/9/parrondo/erwartung.tex b/vorlesungen/slides/9/parrondo/erwartung.tex
new file mode 100644
index 0000000..67bb61d
--- /dev/null
+++ b/vorlesungen/slides/9/parrondo/erwartung.tex
@@ -0,0 +1,76 @@
+%
+% erwartung.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Erwartung}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Zufallsvariable}
+\begin{center}
+\[
+\begin{array}{c|c}
+\text{Werte $X$}&\text{Wahrscheinlichkeit $p$}\\
+\hline
+x_1&p_1=P(X=x_1)\\
+x_2&p_2=P(X=x_2)\\
+\vdots&\vdots\\
+x_n&p_n=P(X=x_n)
+\end{array}
+\]
+\end{center}
+\end{block}
+\begin{block}{Einervektoren/-matrizen}
+\[
+U=\begin{pmatrix}
+1&1&\dots&1\\
+1&1&\dots&1\\
+\vdots&\vdots&\ddots&\vdots\\
+1&1&\dots&1
+\end{pmatrix}
+\in
+M_{n\times m}(\Bbbk)
+\]
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{Erwartungswerte}
+\begin{align*}
+E(X)
+&=
+\sum_i x_ip_i
+=
+x^tp
+=
+U^t x\odot p
+\\
+E(X^2)
+&=
+\sum_i x_i^2p_i
+=
+(x\odot x)^tp
+=
+U^t (x\odot x) \odot p
+\\
+E(X^k)
+&=
+\sum_i x_i^kp_i
+=
+U^t x^{\odot k}\odot p
+\end{align*}
+Substitution:
+\begin{align*}
+\sum_i &\to U^t\\
+x_i^k &\to x^{\odot k}
+\end{align*}
+Kann für Übergangsmatrizen von Markov-Ketten verallgemeinert werden
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From d3b772e811ac42cb912cce367b8e7bee07881084 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 20 May 2021 20:24:26 +0200
Subject: add slides

---
 vorlesungen/slides/9/parrondo/erwartung.tex | 41 ++++++++++++++++-------------
 1 file changed, 23 insertions(+), 18 deletions(-)

(limited to 'vorlesungen/slides/9/parrondo/erwartung.tex')

diff --git a/vorlesungen/slides/9/parrondo/erwartung.tex b/vorlesungen/slides/9/parrondo/erwartung.tex
index 67bb61d..b58c37f 100644
--- a/vorlesungen/slides/9/parrondo/erwartung.tex
+++ b/vorlesungen/slides/9/parrondo/erwartung.tex
@@ -25,6 +25,7 @@ x_n&p_n=P(X=x_n)
 \]
 \end{center}
 \end{block}
+\uncover<4->{%
 \begin{block}{Einervektoren/-matrizen}
 \[
 U=\begin{pmatrix}
@@ -36,9 +37,10 @@ U=\begin{pmatrix}
 \in
 M_{n\times m}(\Bbbk)
 \]
-\end{block}
+\end{block}}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<2->{%
 \begin{block}{Erwartungswerte}
 \begin{align*}
 E(X)
@@ -46,30 +48,33 @@ E(X)
 \sum_i x_ip_i
 =
 x^tp
-=
-U^t x\odot p
+\uncover<5->{=
+U^t x\odot p}
+\hspace*{3cm}
 \\
-E(X^2)
+\uncover<2->{E(X^2)
 &=
-\sum_i x_i^2p_i
-=
-(x\odot x)^tp
-=
-U^t (x\odot x) \odot p
+\sum_i x_i^2p_i}
+\ifthenelse{\boolean{presentation}}{
+\only<6>{=
+(x\odot x)^tp}}{}
+\uncover<7->{=
+U^t (x\odot x) \odot p}
 \\
-E(X^k)
+\uncover<3->{E(X^k)
 &=
-\sum_i x_i^kp_i
-=
-U^t x^{\odot k}\odot p
+\sum_i x_i^kp_i}
+\uncover<8->{=
+U^t x^{\odot k}\odot p}
 \end{align*}
+\uncover<9->{%
 Substitution:
 \begin{align*}
-\sum_i &\to U^t\\
-x_i^k &\to x^{\odot k}
-\end{align*}
-Kann für Übergangsmatrizen von Markov-Ketten verallgemeinert werden
-\end{block}
+\uncover<10->{\sum_i &\to U^t}\\
+\uncover<11->{x_i^k &\to x^{\odot k}}
+\end{align*}}%
+\uncover<12->{Kann für Übergangsmatrizen von Markov-Ketten verallgemeinert werden}
+\end{block}}
 \end{column}
 \end{columns}
 \end{frame}
-- 
cgit v1.2.1

