Solved: A collection of n randomly selected parts is measured twice by an operator using
Chapter 7, Problem 7-63(choose chapter or problem)
A collection of n randomly selected parts is measured twice by an operator using a gauge. Let Xi and Yi denote the measured values for the ith part. Assume that these two random variables are independent and normally distributed and that both have true mean i and variance 2 . (a) Show that the maximum likelihood estimator of 2 is . (b) Show that is a biased estimator for 2 . What happens to the bias as n becomes large? (c) Find an unbiased estimator for 2
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