CS533  Written Homework 4  Due Friday, December 1, 2000 (10:00am)
Consider the following belief network:
The following tables give the conditional probability tables (CPTs) in
each node:
 P(BA) 
A  B=0  B=1 
0  1.0  0.0 
1  0.5  0.5 
 P(CA) 
A  C=0  C=1 
0  0.2  0.8 
1  0.3  0.7 
  P(DB,C) 
B  C  D=0  D=1 
0  0  0.0  1.0 
0  1  1.0  0.0 
1  0  0.4  0.6 
1  1  0.6  0.4 
 Write an algebraic expression for the joint probability
distribution P(A,B,C,D) in terms of the probability
distributions stored in each node.
 Fill in the following table for the joint probability
distribution.
  C=0  C=1 
  D=0  D=1  D=0  D=1 
A=0  B=0  ????  ????  ????  ????

B=1  ????  ????  ????  ???? 
A=1  B=0  ????  ????  ????  ????

B=1  ????  ????  ????  ???? 
 Write an algebraic expression for the probability distribution
P(D) in terms of the probability distributions stored in each node.
 Compute the numerical value of P(D=0).
 Write an algebraic expression for the probability distribution
P(BD) in terms of the probability distributions stored in each
node.
 Compute the numerical value of P(B=0D=0).