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

Each of n specimens is to be weighed twice on the same scale. Let X_i and Y_i denote the two observed weights for the ith specimen. Suppose Xi and Yi are independent of one another, each normally distributed with mean value μ_i (the true weight of specimen i) and variance σ².

a. Show that the maximum likelihood estimator of σ² is