1. Suppose we have X1, . .., Xn ~ f(x; 0), f(x; 0) = aze 202 1 20, 0 otherwise. For the following problems, use the fact (no need to show) that E(X1) = 0, Var(X1) = 4 - 7 ) 02 E(X)) = 04 (a) Find the maximum likelihood estimator of 02, 02MLE. (b) Calculate E[02 MLE]. (c) Find the limiting distribution of X = _ _ _, Xi. That is, find the part (1) and (2) of the following: Vn (X - [ (1) ]) +d N(O, [ (2) 1) (d) Find a constant k such that 0 = X is an unbiased estimator of 0. That is, E(0) = E(KX) = 0. (e) Consider your answer from (d) 0 = kX. Use Chebyshev's inequality to show that as n > OO