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 μi and variance μ2.
(a) Show that the maximum likelihood estimator of σ2 is




(b) Show that is a biased estimator for σ2. What happens to the bias as n becomes large?
(c) Find an unbiased estimator for σ2.

Transcribed Image Text:

ở = (1/4n) E- (X- Y).