CS 4804 Homework #6

1. (10 points) Problem 13.8 from your textbook.
   
   
2. (10 points) Problem 13.10 from your textbook.
   
   
3. (20 points) Problem 13.13 from your textbook.
   
   
4. (40 points) Problem 13.14 from your textbook.
   
   
5. (20 points) In class, we learnt that Bayesian networks encode decompositions of joint probabilities. We discussed Bayesian networks of two variables and showed that there are three distinct possible networks but which correspond to only two distinct distributions of variables. Repeat this exercise for three variables, i.e., identify the number of different Bayesian networks involving three variables (keep in mind that these networks must be directed acyclic graphs) and also identify the number of distinct distributions these networks correspond to.