Merge branch 'master' of raven.am28.uni-tuebingen.de:scientificComputing
This commit is contained in:
@@ -27,4 +27,4 @@ subplot(1, 2, 2);
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plot(psigs, loglm);
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xlabel('standard deviation')
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ylabel('log likelihood')
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savefigpdf(gcf, 'mlestd.pdf', 12, 5);
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savefigpdf(gcf, 'mlestd.pdf', 15, 5);
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Binary file not shown.
@@ -113,8 +113,10 @@ Absch\"atzung der Standardabweichung verdeutlichen.
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\continue
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\question \qt{Maximum-Likelihood-Sch\"atzer einer Ursprungsgeraden}
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In der Vorlesung haben wir eine Gleichung f\"ur die Maximum-Likelihood
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Absch\"atzung der Steigung einer Ursprungsgeraden hergeleitet.
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In der Vorlesung haben wir folgende Formel f\"ur die Maximum-Likelihood
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Absch\"atzung der Steigung $\theta$ einer Ursprungsgeraden durch $n$ Datenpunkte $(x_i|y_i)$ mit Standardabweichung $\sigma_i$ hergeleitet:
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\[\theta = \frac{\sum_{i=1}^n \frac{x_iy_i}{\sigma_i^2}}{ \sum_{i=1}^n
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\frac{x_i^2}{\sigma_i^2}} \]
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\begin{parts}
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\part \label{mleslopefunc} Schreibe eine Funktion, die in einem $x$ und einem
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$y$ Vektor die Datenpaare \"uberreicht bekommt und die Steigung der
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@@ -146,13 +148,12 @@ nicht so einfach wie der Mittelwert und die Standardabweichung einer
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Normalverteilung direkt aus den Daten berechnet werden k\"onnen. Solche Parameter
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m\"ussen dann aus den Daten mit der Maximum-Likelihood-Methode gefittet werden.
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Um dies zu veranschaulichen ziehen wir uns diesmal Zufallszahlen, die nicht einer
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Normalverteilung entstammen, sonder aus der Gamma-Verteilung.
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Um dies zu veranschaulichen ziehen wir uns diesmal nicht normalverteilte Zufallszahlen, sondern Zufallszahlen aus der Gamma-Verteilung.
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\begin{parts}
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\part
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Finde heraus welche Funktion die Wahrscheinlichkeitsdichtefunktion
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(probability density function) der Gamma-Verteilung in \code{matlab}
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berechnet.
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Finde heraus welche \code{matlab} Funktion die
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Wahrscheinlichkeitsdichtefunktion (probability density function) der
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Gamma-Verteilung berechnet.
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\part
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Plotte mit Hilfe dieser Funktion die Wahrscheinlichkeitsdichtefunktion
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@@ -169,17 +170,17 @@ Normalverteilung entstammen, sonder aus der Gamma-Verteilung.
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\part
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Finde heraus mit welcher \code{matlab}-Funktion eine beliebige
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Verteilung (``distribution'') und die Gammaverteilung an die
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Zufallszahlen nach der Maximum-Likelihood Methode gefittet werden
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kann.
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Verteilung (``distribution'') an die Zufallszahlen nach der
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Maximum-Likelihood Methode gefittet werden kann. Wie wird diese
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Funktion benutzt, um die Gammaverteilung an die Daten zu fitten?
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\part
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Bestimme mit dieser Funktion die Parameter der
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Gammaverteilung aus den Zufallszahlen.
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Bestimme mit dieser Funktion die Parameter der Gammaverteilung aus
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den Zufallszahlen.
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\part
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Plotte anschlie{\ss}end
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die Gammaverteilung mit den gefitteten Parametern.
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Plotte anschlie{\ss}end die Gammaverteilung mit den gefitteten
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Parametern.
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\end{parts}
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\begin{solution}
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\lstinputlisting{mlepdffit.m}
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133
statistics/lecture/statistics-slides.tex
Normal file
133
statistics/lecture/statistics-slides.tex
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@@ -0,0 +1,133 @@
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\documentclass{beamer}
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%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\title[]{Scientific Computing --- Statistics}
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\author[]{Jan Benda}
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\institute[]{Neuroethology}
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\date[]{WS 14/15}
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\titlegraphic{\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
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%%%%% beamer %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>
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{
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\usetheme{Singapore}
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\setbeamercovered{opaque}
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\usecolortheme{tuebingen}
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\setbeamertemplate{navigation symbols}{}
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\usefonttheme{default}
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\useoutertheme{infolines}
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% \useoutertheme{miniframes}
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}
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%\AtBeginSection[]
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%{
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% \begin{frame}<beamer>
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% \begin{center}
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% \Huge \insertsectionhead
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% \end{center}
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% \end{frame}
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%}
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\setbeamertemplate{blocks}[rounded][shadow=true]
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\setcounter{tocdepth}{1}
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%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[english]{babel}
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\usepackage{amsmath}
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\usepackage{bm}
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\usepackage{pslatex} % nice font for pdf file
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%\usepackage{multimedia}
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\usepackage{dsfont}
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\newcommand{\naZ}{\mathds{N}}
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\newcommand{\gaZ}{\mathds{Z}}
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\newcommand{\raZ}{\mathds{Q}}
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\newcommand{\reZ}{\mathds{R}}
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\newcommand{\reZp}{\mathds{R^+}}
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\newcommand{\reZpN}{\mathds{R^+_0}}
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\newcommand{\koZ}{\mathds{C}}
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%%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{graphicx}
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\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}}
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%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{listings}
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\lstset{
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basicstyle=\ttfamily,
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numbers=left,
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showstringspaces=false,
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language=Matlab,
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commentstyle=\itshape\color{darkgray},
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keywordstyle=\color{blue},
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stringstyle=\color{green},
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backgroundcolor=\color{blue!10},
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breaklines=true,
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breakautoindent=true,
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columns=flexible,
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frame=single,
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captionpos=b,
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xleftmargin=1em,
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xrightmargin=1em,
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aboveskip=10pt
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}
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\graphicspath{{figures/}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\begin{frame}[plain]
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\frametitle{}
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\vspace{-1cm}
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\titlepage % erzeugt Titelseite
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
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\frametitle{Content}
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\tableofcontents
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\end{frame}
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\subsection{What is inferential statistics?}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
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\frametitle{sources of error in an experiment}
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\begin{task}{Think about it for 2 min}
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If you repeat a scientific experiment, why do you not get the same
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result every time you repeat it?
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\end{task}
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\pause
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\begin{itemize}
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\item sampling error (a finite subset of the population of interest
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is selected in each experiment)
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\item nonsampling errors (e.g. noise, uncontrolled factors)
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\end{itemize}
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\end{frame}
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% ----------------------------------------------------------
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\begin{frame}[fragile]
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\frametitle{statisticians are lazy}
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\Large
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\only<1>{
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\begin{center}
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\includegraphics[width=.8\linewidth]{2012-10-29_16-26-05_771.jpg}
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\end{center}
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\mycite{Larry Gonick, The Cartoon Guide to Statistics}
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}\pause
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\only<2>{
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\begin{center}
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\includegraphics[width=.8\linewidth]{2012-10-29_16-41-39_523.jpg}
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\end{center}
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\mycite{Larry Gonick, The Cartoon Guide to Statistics}
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}\pause
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\only<3>{
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\begin{center}
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\includegraphics[width=.8\linewidth]{2012-10-29_16-29-35_312.jpg}
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\end{center}
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\mycite{Larry Gonick, The Cartoon Guide to Statistics}
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}
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\end{frame}
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