7-Probability and Bayes Nets solutions

# 7-Probability and Bayes Nets solutions - CS 188 Spring 2011...

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CS 188 Spring 2011 Introduction to Artificial Intelligence Section 7 Solutions Probability and Bayes Nets Q1. Green Party President The following Bayes Net describes a hypothetical scenario in which a Green Party presidential candidate may be elected President. In the probability tables below, the values T and F denote true and false. G reen Party President Elected B alanced Budget M arijuana Legalized C lass Attendance Increases P ( G = T ) P ( G = F ) Prior .05 .95 P ( C = T | M ) P ( C = F | M ) M = T .25 .75 M = F .5 .5 P ( B = T | M ) P ( B = F | M ) M = T .8 .2 M = F .2 .8 P ( M = T | G ) P ( M = F | G ) G = T .75 .25 G = F .01 .99 (a) Factor the joint distribution of the variables G, M, B, and C using the chain rule. P ( G, M, B, C ) = P ( G ) P ( M | G ) P ( B | G, M ) P ( C | G, M, B ). Note that this is not the only possible factorization; any ordering of the variables can be used. (b) Now, factor the joint distribution using the simplifying assumptions of this model. P ( G, M, B, C ) = P ( G ) P ( M | G ) P ( B | M ) P ( C | M ) (c) Fill in the full joint probability table below. G M B C P ( G, M, B, C ) true true true true (0 . 05)(0 . 75)(0 . 8)(0 . 25) true true true false (0 . 05)(0 . 75)(0 . 8)(0 . 75) true true false true (0 . 05)(0 . 75)(0 . 2)(0 . 25) true true false false (0 . 05)(0 . 75)(0 . 2)(0 . 75) true false true true (0 .

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