Question: Suppose that X1, . . . , Xn has a Weibull distribution with pdf f(x; ) = 2x 2 e x 2/2 , x 0,

Suppose that X1, . . . , Xn has a Weibull distribution with pdf f(x; ) = 2x 2 e x 2/2 , x 0, where > 0. (a). Prove that this distribution belongs to the regular exponential family. (b). Give a complete sufficient statistic for . (c). One can show that EX 2 = 2 . Find a uniformly minimum variance unbiased estimator for 2 .

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