Question: Let X1, X2, ..., Xn be a random sample of size n from the pdf f (x; 0) = -e-2/0 , x > o. (a)

Let X1, X2, ..., Xn be a random sample of size n from the pdf f (x; 0) = -e-2/0 , x > o. (a) Show that 01 = X1, 02 = X = _, Xi, and 03 = nY1 are all unbiased estima- tors for 0, where Y1 = min(X1, X2, . . ., Xn). [10 marks (b) Find the variances of 01, 02, and 03. [5 marks] (c) Calculate the relative efficiencies of 01 to 03 and 02 to 03. [5 marks] (d) Discuss the consistency of 01, 02, and 03. [5 marks]

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