Artificial Intelligence: Problem Set 5

Assigned: Oct. 24
Due: Oct. 31

Consider the Bayesian network shown below:

In this network, B is independent of A absolutely; D is independent of A and B given C; and E is independent of A, B, and D given C.

Assume that all the random variables are Boolean and that the following probabilities are recorded for the network:

Prob(A=T) = 0.9
Prob(B=T) = 0.5
Prob(C=T | A=T,B=T) = 0.8
Prob(C=T | A=T,B=F) = 0.7
Prob(C=T | A=F,B=T) = 0.7
Prob(C=T | A=F,B=F) = 0.0
Prob(D=T | C=T) = 0.8
Prob(D=T | C=F) = 0.5
Prob(E=T | C=T) = 0.2
Prob(E=T | C=F) = 0.9
Compute the following quantities:
  1. Prob(B=F | A=T).
  2. Prob(C=T).
  3. Prob(B=T | C=T)
  4. Prob(D=T)
  5. Prob(E=T | B=T,C=T).
  6. Prob(E=T | B=T).
  7. Prob(C=F | E=T).