Problem Set 2
ECE534 Spring 2006
Each problem is worth 10 points Due: Feb. 15
Reading Assignment: Chapter 2 of Hajek. Please go through the solutions to the even
numbered problems in the book.
Problems 2.3, 2.5, 2.7, 2.9, 2.11, 2.13, 2.15, 2.17, 2.21,and 2.23 from Hajek.
•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.