Consider estimating an unknown mean from a set of n scalar measurements assumed

to be normally distributed, using a conjugate normal-inverse-gamma prior with parameters 0; ; ; . Derive conditions on the relationship between the prior mean 0 and

the true (unknown) parameter that guarantee that the mean squared error (MSE)

of the Bayesian posterior mean estimator is lower than that of the maximum likelihood

estimator (MLE). Hint: This is best approached by expressing the Bayesian posterior mean as a linear

combination of the MLE and the prior mean.