Problem 4 (20 points) [Normal approximation to posterior under generalized linear models] Suppose we have a random sample yi ~ P0isson()\\,;), i = 1, 2, . . . ,n, where log()\\,;) = (X [3):- and X 6 RM\" and ,6 6 RP. Matrix X is known. However, coefcient [3 is unknown. Suppose n is large. Given a noninformative (i.e. uniform) prior, please derive the approximate multivariate normal distribution to the posterior at the posterior mode. You need to specify the man vector and variance-covariance matrix of this multivariate normal