Question

Problem 3 Consider the following Bayesian Network containing four Boolean random variables. P(A=t) P(B=t) 0.1 0.5 A B P(C=t|A=t) 0.7 P(D=t|A=t,B=t) 0.9 C D P(C=t|A=f) 0.2 P(D=t|A=f,B=t) 0.6 3.a Compute the joint probability P(A=f, B=t, C=f, D=t). P(D=t|A=t,B=f) 0.7 P(D=t|A=f,B=f) 0.3 3.b Compute the posteriori probability P (A = t|B = t, C = t, D = t).

          Problem 3 Consider the following Bayesian Network containing four Boolean random variables.
P(A=t)
P(B=t)
0.1
0.5
A
B
P(C=t|A=t) 0.7
P(D=t|A=t,B=t) 0.9
C
D
P(C=t|A=f) 0.2
P(D=t|A=f,B=t) 0.6
3.a Compute the joint probability P(A=f, B=t, C=f, D=t).
P(D=t|A=t,B=f) 0.7
P(D=t|A=f,B=f) 0.3
3.b Compute the posteriori probability P (A = t|B = t, C = t, D = t).

Problem 3 Consider the following Bayesian Network containing four Boolean random variables.
P(A=t)
P(B=t)
0.1
0.5
A
B
P(C=t|A=t) 0.7
P(D=t|A=t,B=t) 0.9
C
D
P(C=t|A=f) 0.2
P(D=t|A=f,B=t) 0.6
3.a Compute the joint probability P(A=f, B=t, C=f, D=t).
P(D=t|A=t,B=f) 0.7
P(D=t|A=f,B=f) 0.3
3.b Compute the posteriori probability P (A = t|B = t, C = t, D = t).

Added by Miranda L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Rosina Dapaah

Step 1

a To compute the joint probability P(A-f, B-t, C-f, D-t), we can use the chain rule for Bayesian networks: P(A-f, B-t, C-f, D-t) = P(A-f) * P(B-t) * P(C-f|A-f) * P(D-t|A-f, B-t) We have the probabilities from the given information: P(A-f) = 1 - P(A-t) = 1 - 0.1 Show more…

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Problem 3: Bayesian Network and Joint Probability Consider the following Bayesian Network containing four Boolean random variables. P(A=t) P(B=t) 0.1 0.5 P(C=t|A=t) 0.7 P(D=t|A=t,B=t) 0.9 P(D=t|A=f,B=t) 0.6 P(D=t|A=t,B=f) 0.7 P(D=t|A=f,B=f) 0.3 P(C=t|A=f) 0.2 3.a Compute the joint probability P(A=f, B=t, C=f, D=t). 3.b Compute the posterior probability P(A=t|B=t, C=t, D=t).