Question

Q3. [25 pts] Bayesian Net: Inference Given the Bayesian Net in Fig. 2, where each random variable is binary, i.e. x ? {True, False}. Compute the distribution tables for the following probabilities. Show step-by-step derivations clearly in each case. Provide answers accurate to 4 decimal places. X1 p(x1) p(x2) 0.2 0.44 p(x3) 0.2 X2 X3 X4 X5 X? X2 p(X4/X1,X2) X2 X3 p(X5/X2, X3) T T 0.35 T T 0.35 T F 0.6 T F 0.6 F T 0.01 F T 0.01 F F 0.95 F F 0.95 Figure 2: Bayesian Net with Conditional Probability Tables. All probabilities in the above 5 tables are given with respect to the probability of being True given the corresponding configuration of its parents. For example, first row of the table for X4 reads P(X4 =T | X1 =T, X2=T) = 0.35. First row of the table for X2 reads P(X2 = T) = 0.44. Note that, the probabilities of being False and being True always sum up to 1. So, knowing the probability of being True is sufficient to derive the probability of being False. (a) [5 pts] (a) P(x1|x5) Answer:

          Q3. [25 pts] Bayesian Net: Inference
Given the Bayesian Net in Fig. 2, where each random variable is binary, i.e. x ? {True, False}. Compute the
distribution tables for the following probabilities. Show step-by-step derivations clearly in each case. Provide answers
accurate to 4 decimal places.
X1
p(x1)
p(x2)
0.2
0.44
p(x3)
0.2
X2
X3
X4
X5
X?
X2
p(X4/X1,X2)
X2
X3
p(X5/X2, X3)
T
T
0.35
T
T
0.35
T
F
0.6
T
F
0.6
F
T
0.01
F
T
0.01
F
F
0.95
F
F
0.95
Figure 2: Bayesian Net with Conditional Probability Tables. All probabilities in the above 5 tables are given with
respect to the probability of being True given the corresponding configuration of its parents. For example, first row of
the table for X4 reads P(X4 =T | X1 =T, X2=T) = 0.35. First row of the table for X2 reads P(X2 = T) = 0.44.
Note that, the probabilities of being False and being True always sum up to 1. So, knowing the probability of being
True is sufficient to derive the probability of being False.
(a) [5 pts] (a) P(x1|x5)
Answer:

Q3. [25 pts] Bayesian Net: Inference
Given the Bayesian Net in Fig. 2, where each random variable is binary, i.e. x ? True, False. Compute the
distribution tables for the following probabilities. Show step-by-step derivations clearly in each case. Provide answers
accurate to 4 decimal places.
X1
p(x1)
p(x2)
0.2
0.44
p(x3)
0.2
X2
X3
X4
X5
X?
X2
p(X4/X1,X2)
X2
X3
p(X5/X2, X3)
T
T
0.35
T
T
0.35
T
F
0.6
T
F
0.6
F
T
0.01
F
T
0.01
F
F
0.95
F
F
0.95
Figure 2: Bayesian Net with Conditional Probability Tables. All probabilities in the above 5 tables are given with
respect to the probability of being True given the corresponding configuration of its parents. For example, first row of
the table for X4 reads P(X4 =T | X1 =T, X2=T) = 0.35. First row of the table for X2 reads P(X2 = T) = 0.44.
Note that, the probabilities of being False and being True always sum up to 1. So, knowing the probability of being
True is sufficient to derive the probability of being False.
(a) [5 pts] (a) P(x1|x5)
Answer:

Added by Katelyn E.

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