Problem 3: Suppose that X is a discrete random variable with 2 P(X= 0) = 0 P(X= 1) = 2 P(X= 2) = (1-0) P(X = 3) = (1-0) where 0

≤ 0 ≤ 1 is a parameter. The following 10 independent observations were taken from such a distribution: (3, 0, 2, 1, 3, 2, 1, 0, 2, 1). a) Find the method of moments estimate of 0. b) What is the maximum likelihood estimate of 0? c) If the prior distribution of 0 is uniform on [0, 1], what is the posterior density function? d) Find the Bayes Posterior Mean Estimate, the MAP estimate, the Posterior Median Estimate, and a 90% Bayesian Confidence Interval for the parameter 0.