Each of n specimens is to be weighed twice on the same scale. Let Xi and...

Each of n specimens is to be weighed twice on the same scale. Let Xi and Yi denote the two observed weights for the i-th specimen. Suppose Xi and Yi are independent of one another, each normally distributed with mean value µi (the true weight of specimen i) and variance σ 2 . (a) Show that the maximum likelihood estimator of σ 2 is ˆσ P 2 = (Xi−Yi) 2/(4n). [Hint: If ¯z = (z1+z2)/2, then (z1−z¯) 2+(z2−z¯) 2 = (z1 − z2) 2/2.]

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orchestra answered 1 year ago

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