ECE 534 RANDOM PROCESSES FALL 2007
PROBLEM SET 2 Due Wednesday, September 19th
Please visit the course website: http://courses.ece.uiuc.edu/ece534/fall07/index.html
2.Convergence of a Sequence of Random Variables
Assigned reading: Chapter 2 and Sections 8.1-8.3 of the course notes.
Problems to be handed in:
2.3, 2.5, 2.7, 2.9, 2.11, 2.13, 2.15, 2.19, 2.21, and 2.23 from the course notes.
•For problem 2.11, estimate the required probability using the central limit theorem and the
Chernoff bound, and compare these results to the exact probability which can be computed
numerically.
•In problem 2.13(c), if there is not enough information to answer whether certain forms of
convergence take place or not, you can say so.
•For problem 2.21, it may be useful to know that the characteristic function ΦX(u) of a random
variable Xis continuous in u. Thus, if a function is not continuous in u, then it cannot be a
characteristic function.
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