1. Suppose we have X1, . . ., Xn ~ f(x; 0), 2 f(x; 0) = Aze 282, r 20, 0 otherwise. For the following problems, use the fact (no need to show) that E(X1) = OV Var(X1) = 2 E(X] ) = 04 (a) Find the maximum likelihood estimator of 02, 02 MLE. (b) Calculate E[02MLE]. (c) Find the limiting distribution of X = 1 EX;. That is, find the part (1) and (2) of the following: Vn (X - [ (1) ]) +d N(0, [ (2) 1) (d) Find a constant k such that 0 = X is an unbiased estimator of 0. That is, E(0) = E(KX) = 0