Consider the Bayes net shown in Figure S13.12.

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). 

b. Calculate the value of P(b, i, m, ¬g, j). 

c. Calculate the value of P(b, i, ¬m, g, j). 

d. Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor. 

e. A context-specific independence (see page 420) 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 S13.12? 

f. Suppose we want to add the variable P = PresidentialPardon to the network; draw the new network and briefly explain any links you add.

Figure S13.12

B P(B) .9 B .9 M P(G) T TT F TFT TFF FT T FT F FFT FFF 661130601 .0 .0 .2 .1 .0 BM P(I) TT T F FT FF I G J 9 5 5 .1 G TF P(J) .9 .0 P(M) .1 M