Question: help 6.4-12. Let X1,X2,,Xn be a random sample from b(1,p) (i.e., n Bernoulli trials). Thus, Y=i=1nXiisb(n,p) (a) Show that X=Y is an unbiased estimator of

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6.4-12. Let X1,X2,,Xn be a random sample from b(1,p) (i.e., n Bernoulli trials). Thus, Y=i=1nXiisb(n,p) (a) Show that X=Y is an unbiased estimator of p. (b) Show that Var(X)=p(1p). (c) Show that E[X(1X)]=(n1)[p(1p)2]. (d) Find the value of c so that cX(1X) is an unbiased estimator of Var(X)=p(1p)

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