Suppose that X1,...,Xn form a random sample

Chapter 7, Problem 12

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Suppose that X1,...,Xn form a random sample from a distribution for which the p.d.f. is as follows: f (x| ) = 2x 2 for 0 x , 0 otherwise. Here, the value of the parameter is unknown ( > 0). Determine the M.L.E. of the median of this distribution, and show that this estimator is a minimal sufficient statistic for .

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