Find the estimator for p using method of moments

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1. Let X1,...,Xn be a random sample from Geometric distribution with pmf P(X=x) = (1-p)x p, x= 0,1,2,... The mean of this distribution is (1-p)/p.

(a) Find the estimator for p using method of moments.

(b) Find the MLE of p.

(c) Consider a Beta prior on p, i.e.,p∼Beta(α,β). Find the posterior distribution of p.

(d) What is the Bayes estimator of p under squared error loss? Denote it by ˆpB.

(e) What happens to ˆpB if both α a nd β goes to 0?

Reference no: EM132845931

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