3. Let X1, X2, . .., Xn be i.i.d following Uniform(01, 02). (a) Use factorization theorem to show that T = (X(1), X(n) ) is
3. Let X1, X2, . .., Xn be i.i.d following Uniform(01, 02). (a) Use factorization theorem to show that T = (X(1), X(n) ) is sufficient for 0 = (01, 02), where X(1) = min {X1, . .., Xn} and X(n) = max { X1, . .., Xn}. (b) Show T = (X(1), X(n) ) is minimal sufficient. (c) Find MLE of 01 and 02
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