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Unformatted text preview: ECE 5620 Spring 2011 Final Exam: Issued 5/14, Due 5/20 at Noon in the dropbox. Rules: You may consult any written references you wish, including electronic ones, but you must cite them in your solutions . You may not consult people. You may use any result or calculation from the textbook without reproving it. Likewise for any results discussed in class, solved on the homework, on the prelim (or the practice prelims), or as part of a prerequisite course. You must prove any results that you draw from other sources, however. You must show your work to get full credit. Points will be awarded for both the correctness and the brevity of the solu- tion. If your submission contains multiple solutions to a problem, I will select one of them to grade. Complete all six problems. Good Luck! 1 1. When Conditional Independence Implies Independence Suppose that X , Y , and Z satisfy both X Y Z and X Z Y. (a) (4 pts) Does it follow that X is independent of ( Y,Z ) ? Explain. (b) (5 pts) Suppose that X , Y , and Z are finite alphabet and p ( y,z ) > for all y and z . Does it follow that X is independent of ( Y,Z ) ? Explain....
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