[SOLVED] CPS 721 Quiz 10

CPS 721 Quiz 10
2021 Practice Version
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Bayesian Network with Binary Variables

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What is the joint probability distribution of the sample Bayesian network given above, after simplifying using independence?
P(E | C, D) * P(F | C, D) * P(D | A, B, C, E, F) * P(C | B, D, E, F) * P(B | A, C, D) * P(A | B, D) P(E | A, B, C, D) * P(F | A, B, C, D) * P(D | A, B, C) * P(C | A, B) * P(B | A) * P(A)
P(A | B, D) * P(B | C, D) * P(C | D, E, F) * P(D | E, F) * P(E) * P(F)
P(E | C, D) * P(F | C, D) * P(D | A, B, C) * P(C | B) * P(B | A) * P(A)
P(E | D, C) * P(D | C, A, B) * P(C | B) * P(B | A) * P(A) * P(F)
Given that all variables in the Bayesian network are binary (i.e. can take only true/false values), how many numbers are needed to represent the joint probability distribution? Enter an integer only.
Your answer
We are given the values B = true and D = false, and asked to calculate the diagnostic probability that A = true, i.e. P(A = true | B = true, D = false). Applying the formula for conditional probability and marginalization of terms, how many terms and which variables are we summing over in the denominator of the summation?
8 terms, summing over variables C, E, F
16 terms, summing over variables A, C, E, F 4 terms, summing over variables A, C, E, F 4 terms, summing over variables B, D
3 terms, summing over variables A, B, D
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