Question

Each of n specimens is to be weighed twice on the same scale. Let Xi and Yi denote the two observed weights for the ith specimen. Suppose Xi and Yi are independent of each other, each normally distributed with mean value μi (the true weight of specimen i) and variance Ï2.
a. Show that the maximum likelihood estimator of Ï2 is Xi and Yi.

Answer 1

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a) show that the maximum likelihood estimator of Ï2 is Xi and Yi.

attached below is the detailed solution