1. From the joint distribution defined by the graphical model, determine if the conditional independence holds: ALL FIE, B, and provide brief explanation (5 points). 2. Given an undirected chain probabilistic-graphical-model of five nodes in the order, x1, x2. X3, X4, X5. please use the sum-product algorithm to derive the marginal p(x3) from x where x = [X1, X2, X3, X4, xs] (7 points). 3. Suppose we are given a set of N observations of the input vector x, which we denote collectively by a data matrix X whose nth row is x with n = 1,..., N. The corresponding target values are given by =(.....x). The likelihood function is defined as p(t|X. w. p) = II p. x. w. B-1). Please draw the directed probabilistic graphical model corresponding to the likelihood function (5 points). 4. Please briefly explain each step of the general EM algorithm (3 points).