Problem #1 130 points!: Belief Network Consider the following Bayesian network and answer questions. A-H are binary random variables. (a) [5 pts] Which pairs of nodes are independent? (b) [S pts] Are the following conditionally independent a) Cand D given B? b) BandE given D? e Band G given F? d) E and G given H e) A and B given C? (c) [5 pts] Write an expression for the probability P(A-1, B-0,C-O, D-1,E-, F-1,G-1, H-0) in terms of the Bayes Net CPT parameters. Use notation like MB- A-0) to denote specifise parameters in the CPT's (d) [5 pts] Write the samplest expression for the probability PKF-1 I A-I, B-o.c-0, D-1, E-1, G 1) in terms of the Bayes Net CPT parameters. [10 pts] Suppose A, B, C, E are now fixed. We have many observations on D, F, G, and H as shown in the table below. Based on naive Bayesian classifier, if we know F-G-H-0, what is D supposed to be? Illustrate your answer (e) Problem #1 130 points!: Belief Network Consider the following Bayesian network and answer questions. A-H are binary random variables. (a) [5 pts] Which pairs of nodes are independent? (b) [S pts] Are the following conditionally independent a) Cand D given B? b) BandE given D? e Band G given F? d) E and G given H e) A and B given C? (c) [5 pts] Write an expression for the probability P(A-1, B-0,C-O, D-1,E-, F-1,G-1, H-0) in terms of the Bayes Net CPT parameters. Use notation like MB- A-0) to denote specifise parameters in the CPT's (d) [5 pts] Write the samplest expression for the probability PKF-1 I A-I, B-o.c-0, D-1, E-1, G 1) in terms of the Bayes Net CPT parameters. [10 pts] Suppose A, B, C, E are now fixed. We have many observations on D, F, G, and H as shown in the table below. Based on naive Bayesian classifier, if we know F-G-H-0, what is D supposed to be? Illustrate your answer (e)