A sample of N independent observations is taken from a normally distributed population, with N > 2. Denote the N observations by Xh X2, • • •, XN.

You want to estimate the mean of the population, ji. For each of the three estimators G, H, and M, answer the following questions.

G = Xi, H = (Yi + X2)/2, M = (Xi + X2 + • • • + Xn)/N.

(a) Is the estimator sufficient?

(b) Is the estimator unbiased?

(c) Is the estimator consistent?

(d) What is the variance of the estimator?