6.4 Let X, : p × 1 denote a vector representing the response of subject j to a question posed in a sample survey that has p possible response categories, j = 1,...,N. The numbers of subjects in each of the response categories follow a multinomial distribution. Find the posterior distribution for the category probabilities given the observations, under the assumption of a natural conjugate prior distribution. [Hint: See Example (4.4.1).]