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diff --git a/Master/texmf-dist/doc/latex/seminar/semsamp1.tex b/Master/texmf-dist/doc/latex/seminar/semsamp1.tex new file mode 100644 index 00000000000..b6c8a3459ed --- /dev/null +++ b/Master/texmf-dist/doc/latex/seminar/semsamp1.tex @@ -0,0 +1,109 @@ +%% +%% This file may be distributed and/or modified under the conditions of +%% the LaTeX Project Public License, either version 1.2 of this license +%% or (at your option) any later version. The latest version of this +%% license is in: +%% +%% http://www.latex-project.org/lppl.txt +%% +%% and version 1.2 or later is part of all distributions of LaTeX version +%% 1999/12/01 or later. +%% +%% BEGIN semsamp1.tex +% +% This is a sample document for seminar.sty, v0.93 (and maybe later). +% +% Try this with and without the article option: + +\documentclass[fancybox,article]{seminar} + +\def\printlandscape{\special{landscape}} % Works with dvips. + +\articlemag{1} + +%\twoup % Try me. + +\newpagestyle{327}% + {Economics 327 \hspace{\fill}\rightmark \hspace{\fill}\thepage}{}% +\pagestyle{327} + +\markright{Choice under uncertainty} + +\slideframe{Oval} + +\newcommand{\heading}[1]{% + \begin{center} + \large\bf + \shadowbox{#1}% + \end{center} + \vspace{1ex minus 1ex}} + +\newcommand{\BF}[1]{{\bf #1:}\hspace{1em}\ignorespaces} + +\begin{document} + + +\begin{slide} +\heading{A heading} + +One thing this example illustrates is how the {\tt article} style option is +good for printing slides two-up, for distribution to a seminar audience or +class, or just for proofreading. + +\BF{Definition} +$p$ (weakly) first-order stochastically dominates $q$ if for every $\bar z\in +Z$, +\[ + p(z\leq \bar z) \leq q(z\leq \bar z) +\] +\end{slide} + + +\begin{slide} +\heading{Problems with stochastic dominance as a DT} + +\begin{center} + \begin{tabular}{|r|l|}\hline + $z$ & $p(z)$\\ \hline + \$999 & .01\\ \hline + \$1,000,000 & .99 \\ \hline + \end{tabular}% + \hspace{1cm}% + \begin{tabular}{|r|l|}\hline + $z$ & $q(z)$\\ \hline + \$1,000 & 1\\ \hline + \end{tabular} +\end{center} +\end{slide} + +\begin{slide} +\heading{Candidate Theory \#3: Expected utility} + +Let $Z$ be an arbitrary set of outcomes. Let $u:Z\rightarrow R$ be a utility +representation of the DM's preferences over the elements of $Z$ as certain +outcomes. (I.e., $u(y)\geq u(z)$ iff $y \geq z$.) + +\end{slide} + + +\begin{slide} +\heading{Expected utility \& the St.\ Petersburg Paradox} + +This can get around even St.\ Petersburg Paradox, because we don't require +that utility be linear in money: + +\begin{center} + \begin{tabular}{r|c|c|c|c|c}\cline{2-6} + Prize & \$2 & \$4 & \$8 & \$16 & $\ldots$\\ \cline{2-6} + $u(z)=\log_2(z)$ & 1 & 2 & 3 & 4 & $\ldots$ \\ \cline{2-6} + Prob. & 1/2 & 1/4 & 1/8 & 1/16 & $\ldots$\\ \cline{2-6} + \end{tabular} +\end{center} + +Expected utility is $\sum_{k=1}^\infty k/2^k = 2$, and so lottery gives same +expected utility as getting \$4 for sure. +\end{slide} + + +\end{document} +%% END semsamp1.tex |