Question: Consider again a random sample X1, X2, ..., Xn from the distribution . f(x, ) = (1 ) x I{0,1,2,...}(x) a. Does a UMVUE for

Consider again a random sample X1, X2, ..., Xn from the distribution

. f(x, ) = (1 ) x I{0,1,2,...}(x)

a. Does a UMVUE for g() = 1 exist? If no, justify your answer. If yes, find the UMVUE. (3 points)

b. Does a UMVUE for exit? If no, justify your answer. If yes, find the UMVUE. (4 points)

c. Find the MLEs for and 1 and compare these estimators with the corresponding UMVUEs. (3 points)

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