3.18 This exercise shows that the sample variance is an unbiased estimator of the population variance when Y1,c, Yn are i.i.d. with mean mY and variance s2 Y.

a. Use Equation (2.31) to show that E3(Yi - Y )24 = var(Yi ) - 2cov(Yi, Y) + var(Y).

b. Use Equation (2.33) to show that cov(Y, Yi ) = s2 Y>n.

c. Use the results in

(a) and

(b) to show that E(s2 Y) = s2 Y.