1 Consider the Bayes net shown in Figure 23.

a. Which of the following are asserted by the network structure?
(i) P(B, I,M) = P(B)P(I)P(M).
(ii) P(J |G) = P(J |G, I).
(iii) P(M |G,B, I) = P(M |G,B, I, J).

P(B) .9 BIM B P(G) 1 t t t f if t t 0086 .9 BM P(I) t t 9 I f t 1550 M P(M) .1 G P(J) .9 .0 Figure 23 A simple Bayes net with Boolean variables B=Broke Election Law, I = Indicted, M = Politically Motivated Prosecutor, G= Found Guilty, J = Jailed. b. Calculate the value of P(b, i, -m, g,j). c. Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor. d. context-specific independence allows a variable to be independent of some of its parents given certain values of others. In addition to the usual conditional independences given by the graph structure, what context-specific independences exist in the Bayes net in Figure 23? e. Suppose we want to add the variable P = PresidentialPardon to the network; draw the new network and briefly explain any links you add.