Consider the following Bayesian network. This is like Pearl's example except we have one more node TV (whether there is a TV report on earthquake):
Burglary
P(B)
Earthquake
P(E) = 0.002
P(B|E) = 0.001
B E T T
P(A|B, E) = 0.95
P(A|B, ¬E) = 0.94
P(A|¬B, E) = 0.29
P(A|¬B, ¬E) = 0.001
Alarm
E P(TV|E) = 0.90
P(TV|¬E) = 0.01
P(J|A) = 0.90
P(J|¬A) = 0.05
A
P(M|A) = 0.70
P(M|¬A) = 0.01
JohnCalls
MaryCalls
1. (4 pts) Are MaryCalls and TV independent given {Earthquake and Burglary}? Answer this using D-separation.
2. (6 pts) Compute the joint probability of Earthquake and Burglary given MaryCalls and JohnCalls: P(Earthquake, Burglary | MaryCalls, JohnCalls). There is no need to perform numerical calculations. As long as your formula is right, you will get the full mark.