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\centerline{\bf{CALIFORNIA STATE UNIVERSITY, HAYWARD }}
\centerline{\bf{STATISTICS DEPARTMENT}} \centerline{ }
\centerline{\bf{Statistics 6402 Graduate Probability II}}
\centerline{\bf{Winter 2004}}

\medskip
\noindent \centerline{\bf{Take Home Midterm 1}}

\begin{enumerate}
\item
Pick one chapter from Ch.1 - Ch.5 from Suess\&Trumbo. Print the chapter, read the chapter
marking any obvious errors, and turn in the printed out chapter.  Read the problems and
solve one problem of your choice.

\item
Read Ch.6 and Ch.7 from Suess\&Trumbo, do problems 6.13, 7.2, 7.8, 7.11.
Extra Credit, do problems 7.15, 7.16.

\item
Read the paper, Elementary Uses of the Gibbs Sampler: Applications to
Medical Screening Tests, by Suess, Trumbo, and Fraser, available on Blackboard, Gibbs.pdf.
Go to the website for the paper and run the programs from the appendicies and print out the
plots produced in the paper.  Comment on the computer output.  Re-run the analyses
using $N=500$ and $A=16$.  See
\begin{verbatim}
http://www.sci.csuhayward.edu/statistics/Gibbs/
\end{verbatim}

\item
From Ross, Ch. 1, do problem 39, Ch.2 do problem 77, Ch.4 do problem 24

\item
Using jstor from the library website find a current research paper from a journal that
uses MCMC modeling.  Discuss briefly what the model is for and explain how
the Markov Property is used in the model.  Turn in the title of the paper and its author,
along with a link to the paper in jstor.

Another possible online resource for statistics papers is Project Euclid or google scholar.

\begin{verbatim}
http://projecteuclid.org/
\end{verbatim}
\begin{verbatim}
http://scholar.google.com/
\end{verbatim}


\item Short Answer:
\begin{enumerate}
\item
Explain how the gambler's ruin problem can be used to
compare two new drugs developed to treat a certain disease. Hint:
See section 4.5.1 in Ross.
\item
Explain how a Markov Chain can be used to study the simplex algorithm
for solving a linear programming problem. Discuss how Stirling's
approximation is used and how the normal distribution is involved.
Hint: See section 4.5.2 in Ross.
\item
Discuss how to show a Markov Chain is Time Reversible.  Hint:  See section 4.8 in Ross.
\end{enumerate}



\end{enumerate}
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