10 6. (18 points) Bayes’ Nets: The Mind of Pacman Pacman doesn’t just eat dots. He also enjoys pears, apples, carrots, nuts, eggs and toast. Each morning, he chooses to eat some subset of these foods. His preferences are modeled by a Bayes’ net with this structure. A B C D E A E C A E C P C E T N A a) (2 pt) Factor the probability that Pacman chooses to eat only apples and nuts in terms of conditional probabilities from this Bayes’ net. P ( ¬ p,a, ¬ c,n, ¬ e, ¬ t ) = P ( a ) · P ( ¬ p | a ) · P ( ¬ c | a ) · P ( n |¬ p, ¬ c ) · P ( ¬ t |¬ c ) · P ( ¬ e | n, ¬ t ) b) (4 pt) For each of the following properties, circle whether they are true , false or unknown of the distribution P ( P,A,C,N,E,T ) for this Bayes’ net. Without the conditional probability tables, we do not know if any two variables are dependent. From the network topology, we can only conclude true or unknown for the questions below. N
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