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 . (d). Let V = X(1)/X, where X(1) = min{Xi} is the smallest order statistic. Prove that V and Pn i=1 X2 i are independent. (Hint: you may use without proof the fact that the distribution of X/ does not depend on .)