2 let x1 xn be lid uniformly distributed on 01 it was was, Ask an Expert

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2.* Let X1, ... , Xn be lid, uniformly distributed on [0,1]. It was was shown in lecture that a MME estimator of 0 is 9 = 2X, which is an unbiased estimator of O. However, it is not a function of T = max(Xi,.. • , Xn), and T is a sufficient statistic. The Rao-Blackwell theorem says that an unbiased estimator of 0 with smaller variance than 9 is 9 = gOIT). Find 9.

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