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Unformatted text preview: CSCI 5512: Artificial Intelligence II (Spring’10) Homework 1 (Due Mon, Feb 15, 4pm) 1. (20 points) Consider the Burglary network in Figure 1. .001 P(B) .002 P(E) Alarm Earthquake MaryCalls JohnCalls Burglary B T T F F E T F T F .95 .29 .001 .94 P(A|B,E) A T F .90 .05 P(J|A) A T F .70 .01 P(M|A) Figure 1: The Burglary network. (a) (10 points) Using enumeration, compute the probability P ( b | j, ¬ m ), 1 i.e., given John has called and Mary has not called. (b) (10 points) Using variable elimination, compute the probability P ( b, ¬ e | j,m ). 2. (20 points) Consider the Burglary network in Figure 1. Each of the 5 variables in the network is boolean, i.e., can take two possible values. Hence, in order to determine the marginal distributions of each variable, it is sufficient to determine the probability of one of the pos- sible outcomes for each variable. Using the sum-product algorithm, compute the marginal probabilities P ( b ) ,P ( e ) ,P ( a ) ,P ( j ) ,P ( m )....
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