Question 6 (10 marks) [Write your answers in your script book] Consider the Bayes network shown in Figure 6-1, Where C = CommitCrime, A : Arrested, C = FoundGuilty, J = SentToJail and V = TelevisedStory are all Boolean random vari- ables, i.e., they take the value either true (it) or false (f). Also note that P[(:) is shorthand for P(C : true) and P(-wc) is shorthand for P(C : false). P(C} P(V) c A v P(G|C,A,V) 0.9 0.1 t t t 0.9 t t f 0.8 c V P(A|C,V) t f t 0.0 t t 0.9 t f f 0.0 t f 0.5 f t t 0.2 f t 0.5 f t f 0.1 f f 0.1 f f t 0.0 f f f 0.0 G P(JIG) t 0.9 f 0.0 Figure 6-1 (a) [3 marks] Briey explain whether or not the following relationship is consistent with the given network structure? P(C, A, V) = P(C)P(A)P(V) (b) [3 marks] Briey explain whether or not the following relationship is consistent with the given network structure? P(J|G) = P(J|G, A) (c) [4 marks] Calculate the value of P(j|c,a,v). If you cannot easily calculate the nal value, try to simplify the expression as best you can