Homework 5 Due April 26, 2013 


1. Use Metropollis algorithm to simulate a Markov Chain that have the following distribution 
as its stationary/limiting distribution.


The distribution in question is a so called posterior distribution. Its density function is
proportional to the product of 

   ( a.)   a prior distribution that is a beta density, in particular  beta(1, 2) say f(p).

   ( b.)   binomial likelihood, here viewd as a function of p:  (n choose k) p^k (1-p)^(n-k)

           we take n=80, k=36. 

I would like to see your R code. And the final result of the run (say for 9000 steps MCMC).....
as some plots, like a histogram plot etc.

Hint: be careful when p is outside the range (0,1) when coding.

It is probably a good place to reflect, how you will solve the same question but with a prior distribution
other than the beta family. (by computer or by paper and pencil)


2. This question at    www.ms.uky.edu/~mai/sta624/2013HM05.pdf