# HW2-2 - Probabilistic Graphical Models Homework 2 Due April...

• Notes
• 4

This preview shows page 1 - 2 out of 4 pages.

Probabilistic Graphical Models: Homework 2 Due April 28th, (Ordibehesht 9th), beginning of class April 17, 2013 Instructions : There are 3 questions on this assignment. Please submit your homework in the same order they appeared in the homework. 1 Conditional Probability 1.1 [4 pts] Let X , Y , Z be three disjoint sets of variables such that S = X ∪ Y ∪ Z . Prove that P ( X ⊥ Y|Z ) if and only if we can write P in the form: P ( S ) = f ( X , Z ) g ( Y , Z ) 1.2 [5 pts] Is it possible for both f and g above to be probability distributions over their respective sets of variables? Formally, is it possible for every distribution P over ( X ∪ Y ∪ Z ) with the independency above, to be expressed as a product of a distribution over ( Y∪Z )? Justify your answer. ( Hint : look at the marginal probability of Z ; you may assume that the variables are binary if you wish.) 1.3 [3 pts] Prove or disprove (by providing a counter-example) each of the following properties of inde- pendence: 1. ( X Y, W | Z ) implies ( X Y | Z ).

Subscribe to view the full document.

• Spring '13
• Dr.ZAre
• Probability theory, pts, 3 pts, 4 pts, graphical model

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern