thrwawy700 thrwawy700

06-06-2023
Mathematics

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Let X 1 ,X 2 ,…,Xn be iid Bern(p) random variables, so that Y=∑ i=1n X i is a Bin(n,p) random variable. (a) Show that Xˉ =Y/n is an unbiased estimator of p. (b) Show that Var( Xˉ )=p(1−p)/n. (c) Show that E{ Xˉ (1− Xˉ )}=(n−1)[p(1−p)/n]. (d) Find the value of c such that c Xˉ (1− Xˉ ) is an unbiased estimator of p(1−p)/n.

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