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\begin{document}

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\date{January 23, 2003}

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\title{Stat 312: Lecture 3}

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\author{Moo K. Chung\\
mchung@stat.wisc.edu}

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\section*( Definitions}
\begin{enumerate}

\end{enumerate}

{\bf Propositions.} $\bar X$ and $S^2$ are unbiased estimators of $\mu$ and $\sigma^2$ respectively.\\
{\bf In-Class Problems}
Example 6.2.
\begin{verbatim}
> library(Devore5)
> data(xmp06.02)
> attach(xmp06.02)
> mean(Voltage)
[1] 27.793
> max(Voltage)
[1] 30.88
> min(Voltage)
[1] 24.46
> (max(Voltage)+min(Voltage))/2
[1] 27.67}
\end{verbatim}
{\bf Extra Problems}\\
Do it yourself. Example 6.3., 6.4. What is an unbiased estimator of $\mu^2$?\\



{\bf Assignment I} Due Feb 4 11:00am. } Do necessary numerical computations using $\mathbb{R}$.\\ 
Exercise 6.2., 6.4., 6.10, 6.16., 6.20, 6.22.\\
{\em Bonus Problem} (Hard). You are not required to hand in this problem but if you do, you get extra-credit. If $X_i \sim^{i.i.d.} N(0,1)$ and $S^2$ is the sample variance, compute $\mathbb{E}(S^4)$. No partial credit will be given for this problem unless you solve it correctly. 

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