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Let X be a random proportion. Given X=p, let T be the number of tosses till...

Let X be a random proportion. Given X=p, let T be the number of tosses till a p-coin lands heads.

a) Let P(X=1/10)=1/4, P(X=1/7)=1/4, and P(X=1/3)=1/2. Find E(T).

b) Find E(T) if X has the beta(r,s) density for some r>1. Simplify all integrals and Gamma functions in your answer.

c) Let X have the beta(r,s) density. For fixed k>0, find the posterior density of X given T=k. Identify it as one of the famous ones and state its name and parameters.

Math   Statistics-And-Probability   
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