Question: 1. Suppose we have X1, . . ., Xn f(x; 0), f(x; 0) = gze 202, I > 0, 0 otherwise. For the following

1. Suppose we have X1, . . ., Xn " f(x; 0), f(x; 0) = gze 202, I > 0, 0 otherwise. For the following problems, use the fact (no need to show) that E(X 1 ) = 0 Var(X1) = 2 E(XA) = 04 (a) Find the maximum likelihood estimator of 02, 02MLE. (b) Calculate E[02MLE]. (c) Find the limiting distribution of X = 1 ER, Xi. 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. (e) Consider your answer from (d) 0 = kX. Use Chebyshev's inequality to show that 0 - p 0 as n -> Do. (f) Use Delta method to find the limiting distribution of X

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