Consider the following belief network:

with Boolean variables (A = true is written as a and A = false as ¬a, and similarly for the other variable) 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)