Assume (X1 , x2 , •.• , Xn) represents a random sample of size n from a population X with E(X) =µand Var(X) = o2• Assume also that n is even. Consider the estimators x* and Xwhere and Xis the sample...

Assume (X1 , x2 , •.• , Xn) represents a random sample of size n

from a population X with E(X) =µand Var(X) = o2• Assume also

that n is even. Consider the estimators x* and Xwhere

and Xis the sample mean.

(a) Show that x* is an unbiased estimator of µ

(b) Find Var(X*).

(c) Show that the efficiency e(X*, X) is 1/2 for any even

integer n.