100AHW1[1]

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\documentclass[11pt]{article} \input{psfig.sty} \usepackage{epsfig} \ \renewcommand{\baselinestretch}{1.1} %\setcounter{page}{0} \thispagestyle{empty} % \setlength{\topmargin}{-0.60in} \setlength{\oddsidemargin}{-0.2in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9in} \ \def\E{{\rm E}} \def\Var{{\rm Var}} \def\Cov{{\rm Cov}} \ \begin{document} \begin{center} {\huge STAT 100A HWI Due next Wed in class} \end{center} \ \noindent{\bf Problem 1:} Suppose we flip a fair coin 4 times independently. \ (1) What is the sample space? ( (2) What is the set that corresponds to the event that the number of heads is 2? What is its probability? W (3) Let $Z_i = 1$ if the $i$-th flip is head, and $Z_i = 0$ otherwise, for $i = 1, 2, 3, 4$. Let $X$ be the number of heads. Express $X$ in terms of $Z_i$. 2 (4) What is the probability distribution of $X$? That is, what is $\Pr(X=k)$ for $k = 0, 1, 2, 3, 4$? = \noindent{\bf Problem 2:} Suppose we roll a fair die twice independently. Let $X$ and $Y$ be the two numbers we get. a

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## This note was uploaded on 01/29/2010 for the course STATS 100A 262303210 taught by Professor Wu during the Fall '09 term at UCLA.

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100AHW1[1] -...

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