Exercise 6.6 Consider the following belief network:

A B C

E F D

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 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 can be reused? Show the factors that are different from those in part (a).