(d) Now assume that based on historic data. we have a certain expectation for the mean. in the form of a prior distribution p01] 2 7qu Iolroi- Use this extra information to get a better estimate of the underlying mean through Bayesian interenoe: derive the maximum a posteriori estimate, map, that maximizes the posterior probability FUNK)- Consider a data set X = {X},_ of Ni.i.d. samples Xn E R". Assume that the samples follow a multivariate Gaussian distribution with mean / and covariance matrix E, Xn ~N( H. E)