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3. (20 points) Let X1, X2, . .. , Xn be iid from a population with density f ( 20; 0, 1 ) = JONex -0-1 ifx 2/ otherwise, where u > 0 and 0 > 0. (a) (7 points) Show that AMLE = X(1) 1 OMLE = log X - log X(1) where log X = 2 Et_, log Xi. (b) (2 points) Let n = . What is nMLE? (c) (8 points) Assuming no > 1, compute Bias(AMLE), Bias("MLE) in terms of u, 0 and n. (d) (3 points) Assuming ne > 2, compute the mean squared error MSE(AMLE) in terms of M, 0, n. Note: For part (c), you may use the identity (ab + 1)e-ab re " da = b>0. 62