Question: Problem 4[30 pts] Suppose X1, . .., In are a random sample from a distribution with pdf f (x 6) = ge-6(x-10)? 6 > 0.

Problem 4[30 pts] Suppose X1, . .., In are a random sample from a distribution with pdf f (x 6) = ge-6(x-10)? 6 > 0. Justify your solution for each of the question below. (a) [5 pts] Find a univariate sufficient statistic. (b) [6 pts] Compute &mle. (c) [7 pts] Compute the Fisher information In (8). (b) [12 pts] Find an unbiased estimator of 6-1 that has the smallest variance among all unbiased estimators

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