Problem 2 Suppose that X1, ..., Xn ~ iid Bern(p). Part A Find the maximum likelihood estimator for p. Part B Find the method of moments estimator for p. Part C The variance of a Bernoulli distribution is given by p(1 - p) = p - p^2. Compute the maximum likelihood estimator for p(1 - p). Part D Suppose that we want to perform a Bayesian analysis, with pi(p) ~ Beta(a, b). What distribution does the posterior follow? Give a name and parameter(s). Part E What is the resulting Bayes estimator from your posterior in Part D?