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Let X = (X,..., Xn) be a random sample from N(0, 1), where 0 = 0 or 1. Consider the estimation of 0 with

Let X = (X,..., Xn) be a random sample from N(0, 1), where 0 = 0 or 1. Consider the estimation of 0 with action space {0, 1}, i.e., the range of any estimator is {0, 1}. (i) Show that there does not exist any unbiased estimator of 0. (ii) Find an estimator lim, E() = 0. of that is approximately unbiased, that is,

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