Part A: Dirichlet-Multinomial Conjugate Model for Classification . Let r be a discrete variable taking on values {1, 2, ..., K }. The set of probability distributions on a can be param- eterized by a vector u where p(x = k) = /k. The joint probability of N IID samples X = {(1, .... IN} is equal to K P( X | M) = HK Nk k=1 where Nk = Eid(ri = k) and 6(x; = k) is an indicator function. We place a Dirichlet prior over / as follows p( u|a) = Dir(01, . .., OK) A.1. (5 points) Derive the evidence p(X|ox)