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Let p have a uniform prior distribution on 0 1 what is the

Question: Suppose that X follows a geometric distribution,

P(X = k) = p(1 - p)^k-1

and assume an i.i.d. sample of size n.

a. Find the method of moments estimate of p.

b. Find the mle of p.

c. Find the asymptotic variance of the mle.

d. Let p have a uniform prior distribution on [0, 1]. What is the posterior distribution of p? What is the posterior mean?

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