Suppose that the random variable X is normally distributed with mean n and variance a2. Consider the
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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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Related Book For
Statistics Probability Inference And Decision
ISBN: 9780030778056
1st Edition
Authors: Robert L. Winkler, William L. Hays
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