Suppose X1, X2, ...., Xn are i.i.d. Poisson(), with E[X] = and n 2. We have 3 estimators: 1 = (X1 X2)/2, 2 = n n 1 X, 3 = X, where X = 1 n n i Xi. a) (2 pt) Find each estimator's bias, variance and MSE. (0.5 pt each for 1, 3. 1pt for 2) b) (0.5 pt) Which estimators are unbiased? Analyzing just 2 and 3, which estimator has a lower MSE under the following two scenarios? For each scenario, figure out which sample sizes 2 will outperform 3 (or state whether one estimator will always outperform the other under that scenario). Hint: It may help to first calculate an expression for M SE(3) M SE(2), then solve analytically. c) (1 pt) Scenario 1: = 1. d) (1 pt) Scenario 2: = 2.5. e) (0.5 pt) Based on the results in Q1 (c-d), does an unbiased estimator always have a lower MSE than other estimators? Provide a short explanation using the decomposition of M SE in terms of Bias and Variance. (Any reasonable explanation can get full credit