55. 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 s2.

a. Show that the maximum likelihood estimator of s2is [Hint: If 
, then /2.]

b. Is the mle an unbiased estimator of s2? Find an unbiased estimator of s2. [Hint: For any rv Z, E(Z2)  V(Z)  [E(Z)]2. Apply this to Z 
Xi  Yi.]