# Question: Let X1 X2 Xn be a

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

**View Solution:**## Answer to relevant Questions

Let X1, X2, . . . , Xn be a random sample of size n from a normal distribution. (a) Show that an unbiased estimator of σ is cS, where (b) Find the value of c when n = 5; when n = 6. (c) Graph c as a function of n. What is ...Let (a) Show that the maximum likelihood estimator of θ is Find the Rao–Cramér lower bound, and thus the asymptotic variance of the maximum likelihood estimator θ, if the random sample X1, X2, . . . , Xn is taken from each of the distributions having the following pdfs: (a) f(x; ...Consider a random sample X1, X2, . . . , Xn from a distribution with pdf Let θ have a prior pdf that is gamma with α = 4 and the usual θ = 1/4. Find the conditional mean of θ, given that X1 = x1, X2 = x2, . . . , Xn = ...Let S2 be the variance of a random sample of size n from N(μ, σ2). Using the fact that (n − 1)S2/σ2 is χ2(n−1), note that the probability Where Rewrite the inequalities to obtain If n = 13 and Show that [6.11, ...Post your question