1. Consider the Bayesian network in the image attached.If we observe Alarm = true, are Burglary and Earthquake independent? Justify your answer explaining which of the probabilities involved satisfy the definition of conditional independence (no need to perform the actual calculation in class). BurglaryP(B).001AlarmA P(J)JohnCalls 1 .90f.05EarthquakeBEP(A)tt951f94f129f f .001MaryCallsP(E).002A P(M)1 .70f .01Figure 1 - A typical Bayesian network, showing both the topology and theconditional probability tables (CPTS). In the CPTS, the letters B, E, A, J, and Mstand for Burglary, Earthquake, Alarm, JohnCalls, and MaryCalls, respectively.

We are given here that:P(B) = 0.001,P(E) = 0.002 Using law of total probability, we have here:P(A) =…

Burglary JohnCalls P(B) .001 Alarm A P(J) 90 f .05 Earthquake B t 1 f f f E t f 1 P(A) 95 94 29 .001 MaryCalls P(E) 002 A P(M) 1.70 f .01 Figure 1 - A typical Bayesian network, showing both the topology and the conditional probability tables (CPTS). In the CPTS, the letters B, E, A, J, and M

Burglary JohnCalls P(B) .001 Alarm A P(J) 90 f .05 Earthquake B t 1 f f f E t f 1 P(A) 95 94 29 .001 MaryCalls P(E) 002 A P(M) 1.70 f .01 Figure 1 - A typical Bayesian network, showing both the topology and the conditional probability tables (CPTS). In the CPTS, the letters B, E, A, J, and M

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section: Chapter Questions

Problem 16RP

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Question

1. Consider the Bayesian network in the image attached.

If we observe Alarm = true, are Burglary and Earthquake independent? Justify
your answer explaining which of the probabilities involved satisfy the definition of
conditional independence (no need to perform the actual calculation in class).

Burglary
P(B)
.001
Alarm
A P(J)
JohnCalls 1 .90
f.05
Earthquake
B
E
P(A)
t
t
95
1
f
94
f
1
29
f f .001
MaryCalls
P(E)
.002
A P(M)
1 .70
f .01
Figure 1 - A typical Bayesian network, showing both the topology and the
conditional probability tables (CPTS). In the CPTS, the letters B, E, A, J, and M
stand for Burglary, Earthquake, Alarm, JohnCalls, and MaryCalls, respectively.

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