Let Y1, Y2,..., Yn denote a random sample of size n from a population with a uniform

Chapter 8, Problem 8.18

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Let Y1, Y2,..., Yn denote a random sample of size n from a population with a uniform distribution on the interval (0, ). Consider Y(1) = min(Y1, Y2,..., Yn ), the smallest-order statistic. Use the methods of Section 6.7 to derive E(Y(1)). Find a multiple of Y(1) that is an unbiased estimator for .

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