University of Illinois
Fall 2011
ECE 534: Exam II
Monday November 14, 2011
7:00 p.m. 8:15 p.m.
103 Talbot
1. [15 points] Suppose Xt = V exp(U t) where U and V are independent, and each is uniformly
distributed over the interval [0, 1].
(a) Find the mean f

ECE 534: Random Processes
Spring 2013
HW VII
R. Srikant
1. Consider a discrete-time queueing system with Ber() arrivals and Ber() service with < .
Assume departures occur before arrivals in each time slot.
(a) Write down the queueing dynamics of this syst

ECE 534: Random Processes
Spring 2011
Solutions to Midterm
1. Let cfw_Xn be a sequence of d dimensional vectors and let X be a random vector, all dened
2
on the same sample space. The Euclidean norm of a vector v Rd is v = ( d vi )1/2 .
i=1
We say that c

ECE 534: Random Processes
Fall 2010
Solutions to Midterm 1
1. The pair of random variables (Xn , Yn ) R2 converges in some sense (a.s., or m.s., or d.)
to (X, Y ) as n . Dene Zn = Xn + Yn and Z = X + Y . Are the following three
statements true?
d
(Xn , Y

ECE 534: Random Processes
Fall 2010
Solutions to Midterm 2
1. You are given the magnitude of a normal random variable X N (0, 1). Find the
estimator X = a + b|X| that minimizes MSE = E[(X X)2 ], and give the resulting
MSE.
Solution: We have
Cov(X, |X|)
X

ECE 534: Random Processes
Spring 2013
Probability Review Quiz
R. Srikant
Feb 7 2013, 7:00-8:15
Each problem is worth 25 points. No calculators allowed; you are allowed two sheets of handwritten
notes.
1. Consider the following CDF of a random variable X:

ECE 534: Random Processes
Spring 2011
Solutions to Probability Review Quiz
1. Suppose youre on a game show and given a choice of three doors. A car is behind one of
the doors with equal probability. After you pick a door, the host opens one of the other
t

University of Illinois Spring 2011
ECE534 Moulin
Final Exam
Monday, May 9, 2011
Sow-ﬂow SET
Name
Score
Please do not turn this page until requested to do so.
You may use three cheat sheets for this exam. Make sure to show all of your work on the longer
pr