Question: Let X1, X2, . . . , Xn be a random sample from b(1, p) (i.e., n Bernoulli trials). Thus, (a) Show that = Y/n

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

(a) Show that = Y/n is an unbiased estimator of p.
(b) Show that Var(X) = p(1 ˆ’ p)/n.
(c) Show that E[(1 ˆ’ X)/n] = (n ˆ’ 1)[p(1 ˆ’ p)/n2].
(d) Find the value of c so that c(1 ˆ’ ) is an unbiased estimator of Var() = p(1 ˆ’ p)/n

YX is b(n,p). i-1

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