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Suppose that (X1, · · · , Xn) is a random sample from uniform distribution U(0,...

Suppose that (X1, · · · , Xn) is a random sample from uniform distribution U(0, θ).

(a) Prove that T(X1, · · · , Xn) = X(n) is minimal sufficient for θ. (X(n) is the largest order statistic, i.e., X(n) = max{X1, · · · , Xn}.)

(b) In addition, we assume θ ≥ 1. Find a minimal sufficient statistic for θ and justify your answer.

Math   Statistics-And-Probability   
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