Question: Suppose that the random variable X is normally distributed with mean n and variance a2. Consider the following two estimators of n, based on a

Suppose that the random variable X is normally distributed with mean n and variance a2. Consider the following two estimators of n, based on a sample of four independent observations, Xi, X2, X3, and X4:

G = (Xi + X2 + X3 + X4)/4 H = (4Ah 3X2 + 2X3 + X4)/10.

(a) Is G unbiased?

(b) Is H unbiased?

(c) Find the variance of G and the variance of H.

(d) Which of the two estimators is more efficient? What is the relative efficiency?

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