1.
In the Bayesian Network below, the variables are A, B, C, D, E, and they are all Boolean. In the CPTs,
the notation P(a) denotes the probability that A is set to True, with similar meanings for P(b), P(c), etc.
Use variable elimination to determine the probability distribution over A given the observations that D
is False and E is True. You may eliminate variables in any order you wish, but please show your
work. (If you have neither a calculator nor time to perform the computations, then please simply write
out in full the arithmetic expressions to be evaluated.)
2.
Given the following Bayes net, build a junction tree. Perform the upward and downward passes
given the evidence that B is true and F is false. What is the distribution over A? What about over C?
A
A
T
F
P(b)
0.6
0.3
B
C
D
B
T
F
P(d)
0.7
0.1
P(a)
0.2
B
F
F
T
T
F
F
T
T
C
F
T
F
T
F
T
F
T
P(c)
0.7
0.1
F
E
A
F
F
F
F
T
T
T
T
A
T
F
P(e)
0.2
0.1
0.3
0.1
0.5
0.8
0.6
0.9
C
T
F
P(f)
0.5
0.9
3.
Given the following Bayes Net, construct the corresponding junction tree (ignore conditional
probability tables).
A
B
D
C
G
I
4.
F
E
H
J
Given the same Bayes Net in question 3, suppose we have evidence at nodes E and F, but
nowhere else. Which nodes are d-separated from node C?