1. We are given the following Bayesian network over X2, X3, …, X9. Note that there is no X1.
a. What is the Bayesian network factorization of the joint P(X2, X3, …, X9)?
b. Assume Xi can take i possible values (for e.g., X2 is binary, X3 can take on 3 possible values, …, X9 can take on 9 possible values)
i. What is the number of independent parameters required to represent the full joint using the naïve table representation? Show your work. ii. What is the number of independent parameters required for this network? Show your work.
c. For each of the following independence statements, indicate whether it is True or False. i. X2 ⊥ X3
ii. X2 ⊥ X3 | X8 iii. X2 ⊥ X3 | X6 iv. X2 ⊥ X4 | X9
v. X7 ⊥ X6
2. We are given the following Bayesian network. Please compute the requested probabilities using variable elimination.
a.P(B)
b. P(C|A=T)
c. P(A, B | C=T, D=F).
3. We are given the following decision network.
a. What action should you take?
b. What is the value of information of Z?
c. What is the value of information of X?
d. Given Z=T, what is the value of information of X?
