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(a) Show how to find the marginal probability P(A, D). (e) Using the conditional probability distribution (CPD) tables in the figure, find: i. Pla – 116 - 0) ii. Pla – 1,0 -0) iii. P(a – 1,6 - 0,0–0,2 – 0,2-0, f – 0,9 - 1) iv. P(6-0,6-0,6-0, f -0,9 – 110 – 1,0 – 0)

4. (25 points) Consider the Bayesian Network below: a=0 0.2 a=1 0.8 A bob=1 a=0 0.9 0.1 a=10.5 0.5 c=01 C=1 a=0.5 0.5 a=1025 0.75 B f0f=1 c=0 0.5 0.5 c=10.802 D E F d=0 d=1 b=0 0.703 b=1 02 08 G e=0 0.8 0.9 0.5 0.6 b=1, C=0 b=1, C=1 b=1,c=0 b=1, c=1 Olololo H|Jთი e=1 02 0.1 05 0.4 g=0g=1 e=0 0.7 0.3 e=10.5 0.5 Note: The numerical values of the probabilities are for part (e). You do not need to use them for (a)-(a). (a) Find the joint probability P(A,B,C,D, E, F, G) as the product of conditional probabilities, according to the graphical model given above. (b) List all conditional independence given the graph. (c) Show how to find the conditional probability P(AC).