ECE 534 RANDOM PROCESSES FALL 2006
PROBLEM SET 3 Due Monday, Oct 9th
Please visit the course website: http://courses.ece.uiuc.edu/ece534/fall06/
3. Random Vectors and Minimum Mean Squared Error Estimation
Assigned reading: Chapter 3 and Section 8.6, Matrices, in the Appendix of the course notes.
Problems to be handed in:
3.1, 3.3, 3.5, 3.7, 3.11, 3.15, 3.17, 3.19, and 3.21 from the course notes.
•Problem 3.3: Can E(X|Y) be negative?
•Problem 3.7: You dont have to answer the question about uniqueness in part (b). The answer
is non-unique; it may be useful for you to think of an example to show that the answer is
non-unique, but you dont have to do it as part of the homework.
•Problem 3.19: The fact that bounded monotone sequences converge may be useful to prove
(a). A monotone sequence is a sequence that is either non-increasing or non-decreasing.
Course notes:
B. Hajek, An Exploration of Random Processes for Engineers, July 30, 2006.
Available for download at
http://www.ifp.uiuc.edu/~hajek/Papers/randomprocesses.html
and also available for purchase in 243 Everitt Lab.
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