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\begin{document}
\title{Stat 150 Homework \#10}
\author{Spring 2022}
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\textbf{NOT DUE}\\

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\item Durrett 5.4 (there is a typo in the statement of part (b): you should show that $(1/n)\log Y_n \to -1$). Hint: you will need to remember some calculus. The point of the exercise is that $M_n \to 0$ almost surely even though $\E[M_n] = 1$ for all $n$, hence the ``unfair fair game''. Of course, you know by now that expected value does not tell the complete story.

\item Durrett 5.6 (Hint: assume that $\sigma^2 > 0$ since otherwise the statement is trivial. What can you say about $\pr(T < \infty)$?)
  
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