Question 3: Exam type problem Suppose that X = (X1,...,Xk) is Multinomial with X | 6 ~ M1902, 61,62,...,6k). Now assume that 0 has a prior distribution With density we) 0: 0?1'16'2'1.--6,j""1 with expectation 051' 011 + ' ' ' + 0k. Suppose that you are given a vector of observation X = x. This prior distribution is also called the Dirichlet Distribution. E [0i] . Calculate the posterior distribution of 6 | x. . What is the Bayes estimator for Bi under the squared error loss? Bayes Estimator under Squared Error Loss Theorem: Let L(9, a) = (6 a)2. Let 6 be a real-valued parameter and suppose that the posterior mean of 6 is nite. Then, a Bayes estimator of 6 is 6*(x) = 5(9 | x)