# Question

Let X1, X2, . . . , Xn be a random sample from b(1, p) (i.e., n Bernoulli trials). Thus,

(a) Show that = Y/n is an unbiased estimator of p.

(b) Show that Var(X) = p(1 − p)/n.

(c) Show that E[(1 − X)/n] = (n − 1)[p(1 − p)/n2].

(d) Find the value of c so that c(1 − ) is an unbiased estimator of Var() = p(1 − p)/n

(a) Show that = Y/n is an unbiased estimator of p.

(b) Show that Var(X) = p(1 − p)/n.

(c) Show that E[(1 − X)/n] = (n − 1)[p(1 − p)/n2].

(d) Find the value of c so that c(1 − ) is an unbiased estimator of Var() = p(1 − p)/n

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