\def\Line{\hbox to \hsize} \def\handout#1#2{ \Line{University of Washington\hfil\today} \Line{Department of Computer Science and Engineering\hfil} \Line{CSE 321, Fall 1994\hfil} \Line{Handout No. #1\hfil} \vskip45pt \centerline{\vbox{\hbox{#2}\vskip2pt\hrule}}} \def\problem#1{\goodbreak\bigskip\noindent{\bf Problem #1:}\par\smallskip} \def\extra#1{\goodbreak\bigskip\noindent{\bf Problem #1 [Extra Credit]:}\par\smallskip} \def\solution{\goodbreak\medskip\noindent{\bf Solution:}\par\smallskip} \def\note{\goodbreak\smallskip\noindent{\bf Note:}\par\smallskip} \def\margin#1{\hbox to 0pt{\hss #1\quad}} \documentstyle[11pt, fullpage]{article} \parindent=0pt \pagestyle{empty} \begin{document} \handout{13}{{\bf Homework 7, Due Monday, November 14}} \bigskip (Friday, November 11 is a holiday.) Read - 4.6, 6.1, 6.2 (Chapter 5 will not be covered) \bigskip \problem1 Page 256, Problem 12, Problem 16 \problem2 Page 256, Problem 22 (What he is trying to say is $1\le k \le 100$). \problem3 Page 270, Problem 14 \problem4 Page 270, Problem 20 \problem5 Consider the following game that is offered at Anderson's Casino: Initially, you start out with \$1. A coin is flipped, if it is heads you double your money and play again, if it is tails the game stops, and you keep your money. You know that the Casino is a somewhat sleazy place, infact, you know that the probability that the coin comes up heads is$1\over 3$, and the probability it comes up tails is$2\over 3$. \begin{itemize} \item[a)] What is the probability that you have exactly$\$2^k$ when the game stops? \item[b)] Give a formula that can be used to compute your expected winnings when you play this game. \item[c)] Evaluate your formula to determine your expected winnings. \item[d)] The Casino charges \$3 to play this game (although it does provide you with the initial \$1). Do you play? \end{itemize} \problem6 The state gaming commission has closed Anderson's Casino inorder to promote the well being of the citizenry, and to reduce competition to the state lottery. As the new owner, you are allowed to reopen the Casino, with the requirement that you use a fair coin in the game, so the probability of heads is $1\over 2$, and the probability of tails is $1\over 2$. You are allowed to set a new charge to play this game to reflect the change in expected winnings because of the fair coin. How much do you charge bettors, so that the Casino expects to make a profit? Justify your answer. \end{document}