## Description

Please submit your solutions through blackboard assignment page.

- We are given the following Bayesian network over
*X*2,*X*3, …,*X*9. Note that there is no*X*1.

** **

- What is the Bayesian network factorization of the joint P(
*X*2,*X*3, …,*X*9)?

** **

- Assume
*X**i*can take*i*possible values (for e.g.,*X*2 is binary,*X*3 can take on 3 possible values, …,*X*9 can take on 9 possible values)

** **

- What is the number of independent parameters required to represent the full joint using the naïve table representation? Show your work.

- What is the number of independent parameters required for this network? Show your work.

- For each of the following independence statements, indicate whether it is True or False.

** **

*X*2⊥*X*3

*X*2⊥*X*3|*X*8

*X*2⊥*X*3|*X*6

*X*2⊥*X*4|*X*9

*X*7⊥*X*6

- We are given the following Bayesian network. Please compute the requested probabilities using variable elimination.

** **

** **

** **

** **

** **

** **

** **

- P(B)

** **

- P(C|A=T)

** **

- P(A, B | C=T, D=F).

- We are given the following decision network.

** **

- What action should you take?

** **

- What is the value of information of Z?

** **

- What is the value of information of X?

** **

- Given Z=T, what is the value of information of X?