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 one another, each normally distributed with mean value mi (the true weight of specimen i) and variance σ2.
a. Show that the maXimum likelihood estimator of σ2 is σ2 = Σo(Xi - Yi)2 = (4n).
b. Is the mle σ2 an unbiased estimator of σ2? Find an unbiased estimator of σ2.