2. Consider the Bayesian network in Figure it (a) Express Pr(A, B , C, D, E, F, G , H ) as a multiplication of conditional and marginal probabilities, according to the factorization encoded in the network structure. (b) Express Pr(E,F, G,H) in terms of factors instead of (conditional) probabilities. (c) Express Pr(a,ub,c,d,-e,f,ug, h) in terms of the parameters in the CPTs (0. denotes A = 1 and uo. denotes A = 0). Use placeholder symbols for the parameters that are not shown in the CPTs. ((1) Compute Pr(-a, b) and Prhe | a). Justify your answers. Hint: leaf nodes that are not part of the probability query can be removed from the network without affecting the computed probability. (9) List the Markovian assumptions (also known as topological semantics) encoded in the Bayesian network structure. (f) Provide the Markov blanket for variable D. (g) Multiply the factors (tables) corresponding to Pr(D|AB) and Pr(E|B).| (h) Sum out D from the factor (table) computed above. A B D E F G H BE Pr(E B) A Pr(A) B Pr(B) 1 8 O O .3 0 OHO 0 A B D Pr(DAB) OHOH O DOO O HHH OOHH OHOH Figure 1: A Bayesian network with some of its CPTs