10. Consider the following belief network:

with Boolean variables (we write A = true as a and A = false as ¬a) and the following conditional probabilities:

P

(a) = 0.9 P

(b) = 0.2 P(c ∣

a, b) = 0.1 P(c ∣

a, ¬b) = 0.8 P(c ∣ ¬a,

b) = 0.7 P(c ∣ ¬a, ¬b) = 0.4 P(d ∣

b) = 0.1 P(d ∣ ¬b) = 0.8 P(e ∣

c) = 0.7 P(e ∣ ¬c) = 0.2 P(f ∣

c) = 0.2 P(f ∣ ¬c) = 0.9

(a) Compute P

(e) using variable elimination (VE). You should first prune irrelevant variables. Show the factors that are created for a given elimination ordering.

(b) Suppose you want to compute P(e ∣ ¬f) using VE. How much of the previous computation is reusable? Show the factors that are different from those in part (a).