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**cm917** X is a discrete RV with P(X=1) = p , P(X=2)=1-p; three independent observations of X are made x1=1, x2=2,x3=2.

a)find the method of moments estimate of p

In order to find the method of moments estimate of p, I know I need to find the 1st moment and the 2nd moment.

What I did is.... E(p) = 1/3 p +2/3 (1-p) ...am I on the right track? when I continue to find the 2nd moment E(p square)...it turns out weird... the final answer for this question is 1/3.

d) if p has a prior distribution that is uniform on [0,1], what is its posterior density?

Actually, I have difficulty in finding the posterior density. If anyone could do it as an exmaple for me. That would be perfect. Thanks!