Question

a) Consider the following Bayesian Network containing four Boolean random variables. $P(A)$ A B $P(B)$ 0.5 $P(C \mid A)$ 0.7 C D $P(D \mid A, B)$ 0.9 $P(C \mid A)$ 0.2 $P(D \mid A, B)$ 0.6 $P(D \mid A, B)$ 0.7 $P(D \mid A, B)$ 0.3 1) List all independence and conditional independence relationships implied by this Bayesian Network? [3 marks] 2) Compute $P(A, B, C, D)$ [3 marks] 3) Compute $P(C \mid A, B)$ [2 marks] 4) Compute $P(A \mid B, C, D)$ [5 marks]

          a) Consider the following Bayesian Network containing four Boolean random variables.
$P(A)$
A
B
$P(B)$
0.5
$P(C \mid A)$ 0.7
C
D
$P(D \mid A, B)$
0.9
$P(C \mid A)$ 0.2
$P(D \mid A, B)$
0.6
$P(D \mid A, B)$
0.7
$P(D \mid A, B)$
0.3
1) List all independence and conditional independence relationships implied by this
Bayesian Network?
[3 marks]
2) Compute $P(A, B, C, D)$
[3 marks]
3) Compute $P(C \mid A, B)$
[2 marks]
4) Compute $P(A \mid B, C, D)$
[5 marks]

a) Consider the following Bayesian Network containing four Boolean random variables.
P(A)
A
B
P(B)
0.5
P(C | A) 0.7
C
D
P(D | A, B)
0.9
P(C | A) 0.2
P(D | A, B)
0.6
P(D | A, B)
0.7
P(D | A, B)
0.3
1) List all independence and conditional independence relationships implied by this
Bayesian Network?
[3 marks]
2) Compute P(A, B, C, D)
[3 marks]
3) Compute P(C | A, B)
[2 marks]
4) Compute P(A | B, C, D)
[5 marks]

Added by David C.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

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Solved by Expert Tanvi Garg

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Texts: I need to solve this question. a) Consider the following Bayesian Network containing four Boolean random variables: PA PB) 0.5 P(C|A) 0.7 P(C|A) 0.2 PD|A,B PD|A,B P(D|A, B) PD|A,B) 0.9 0.6 0.7 0.3 1) List all independence and conditional independence relationships implied by this Bayesian Network? [3 marks] Compute P(A,B,C,D) [3 marks] Compute P(C|A,B) [2 marks] 4) Compute P(A,B,C,D) [5 marks]