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[Solved]: Let {X1, X2, . . . , Xn} be a random sample from a
Home / Expert Answers / Statistics and Probability / let-x1-x2-xn-be-a-random-sample-from-an-exponential-distribution-with-parameter-this-pa578

(Solved): Let {X1, X2, . . . , Xn} be a random sample from an Exponential distribution with parameter . This ...



Let {X1, X2, . . . , Xn} be a random sample from an Exponential distribution with parameter ?. This means that E(Xi) = ? and V (Xi) = ? 2 for all i = 1, 2, . . . , n. We propose three estimators for estimating ? as: T1 = X1 + X2 2 , T2 = X1 + X2 + X3 3 , T3 = X1 + X2 + X3 + X4 4 . Which one is unbiased and has the smallest variance among these three estimators? (A) T1 (B) T2 (C) T3 (D) both T1 and T2



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