Consider again a random sample X1,..., Xn from the population distribution with density f (x; 0) = 0xº-1, x € (0, 1), and parameter 0 E (0, 00), as in Q2. (1) Is the above parametric model an exponential family? Justify your answer. (2) Is there an unbiased estimator of 0 whose variance reaches the Cramér-Rao lower bound? Justify your answer. (3) Show that T = -(1/n) E log(X;) is sufficient for 0.

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