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Problem 7. Let X1,..., X, be independent random variables with common density Po(I) = 0, otherwise, for some positive 0. Set T = >,_, log(Xj).

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Problem 7. Let X1,..., X, be independent random variables with common density Po(I) = 0, otherwise, for some positive 0. Set T = >,_, log(Xj). (1) Show that T is a complete and sufficient statistic. (2) Find the distribution of 7. Hint: Start by finding the distribution of log( X1). (3) Find a BUE of 1/0. (4) Find a BUE of 0

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