1. Suppose that the heights of the individuals from a certain population have a normal distribution for which the mean is unknown but the variance ^2 is known. Let 1 be the M. L.E. and 2 be the Bayes estimator of , for which the prior distribution is also a normal distribution with mean 68 inches and standard deviation 2 inches.

(a) Is the Bayes estimator unbiased (conditioning on the value of ) ? If not, find its bias.

(b) Compare the M. L. E with the Bayes estimator for the squares loss function.