Graphical Models:  Assignment 2
Due February 6, 2017
(extended to February 7, 2017)

  1. Answer the following true/false questions about the Bayesian network shown below.  Explain your reasoning. Picture has been corrected.
    1. K is independent of A given F.
    2. F d-separates A from B and D.
    3. E is independent of H given B.
    4. B is independent of C given G and H.
    5. J is independent of D given E, H and C.
BN picture
  1. Find the Markov blanket of F.  Find the Markov blanket of E.  Explain your reasoning.
  2. How many probabilities would be needed to define a fully specified joint distribution on 25 random variables with 4 states per random variable?  How many probabilities are needed for a Bayesian network with one root node, two nodes with one parent, and the rest of the nodes with two parents? 
  3. Repeat Problem 3 with 100 random variables with 10 states per random variable.  Find the general formula for the answer to Problem 3 if there are n random variables with k states per random variable.