Suppose that we observe X1, ..., Xn iid Bern(p).

Part 1

Suppose that we want to perform a Bayesian analysis with (p) Beta(.5, .5). Com- pute the posterior (p|X). Using this posterior, find a Bayes estimator for p.

Part 2

Compute the MSE for the MLE and Bayes estimators. Find respective intervals where each estimator performs better.