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Problem 5: Unbiased estimators and Relative Efficiency (30 points) Suppose X1, X2, X3 are a random sample of size 3 from an exponentional distribution X ~ Exp(0) with pdf f(x) = (1/0)e-x/0 for x > 0, 0 > 0. Let 01 = X1, 02 = ( XitX2) 2 and 03 = (X1+2X2) 3 a. (15 points) Show that these estimators of 0 are all unbiased. b. (15 points) Determine the relative efficiencies between them and find which estimator is the most efficient