Question: Let X1, . . . , Xn be i.i.d. from Uniform distribution on the interval (1, 1 + 2), where 1 R, 2 > 0.

Let X1, . . . , Xn be i.i.d. from Uniform distribution on the interval (1, 1 + 2), where 1 R, 2 > 0. both 1 , 2 unknown.

Find UMVUE of 2, by proving unbiased statistics or conditional expectation.

(Hint: The jointly complete sufficient statistics for 1, 2 are the order statistics X(1), X(n) . You can use this fact without proof.)

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