10-19. Let X1, . . . ,Xn be a random sample drawn from a N(, ) probability...

10-19. Let X1, . . . ,Xn be a random sample drawn from a N(μ, σ) probability density function. Maximum likelihood estimators for μ and σ2 are X and S2 1

= 1n

ni

=1 (Xi − X)2, respectively. Demonstrate that X is an unbiased estimator for μ and S2 1 is a biased estimator for σ2. Find the mean squared error for both X and S2 1.