University of Illinois
Spring 2010
ECE 313:
Problem Set 4
Counting Random Variables, MaximumLikelihood Estimation
Due:
Wednesday February 17 at 4 p.m.
Reading:
Ross
Chapter 4.
Noncredit Exercises:
Chap. 4: Problems 32, 3839, 4043, 4752;
Theoretical Exercises 10, 11, 1320, Selftest problems 1114
1.
[The Binomial Random Variable I]
Consider a football game in where the offense has 5 offensive linemen lined up at the line of
scrimmage. An offensive lineman will move before the ball is snapped  resulting in a false
start  independently of any other lineman with probability 10

3
.
(a) Specify the probability of a false start,
p
fs
on any offensive play
(b) Suppose a typical football game has 100 offensive snaps in a game. Specify the pmf for
the random variable
X
denoting the number of false starts in the game.
(c) A false start results in loss of 5 yards on any play. What is the expected amount of total
yards in penalty incurred during a game?
2.
[Geometric Random Variables]
During a bad economy, a graduating ECE student goes to career fair booths in the technology
sector (e.g.
Google, Apple, Qualcomm, Texas Instruments, Motorola, etc)  and his/her
likelihood of receiving an interview request after a career fair booth visit depends on how
well he/she did in ECE 313. Specifically, an A in 313 results in a probability
p
A
= 0
.
95 of an
interview, whereas a C in 313 results in a probability of
p
B
= 0
.
15 of an interview.
(a) Give the pmf for the random variable
Y
that denotes the number of career fair booth
visits a student must make before his/her first interview invitation.
(b) On average, how many booth visits must an A student make before getting an interview,
as compared to a C student?
(c) Suppose that during a typical career fair, there are a total of 5 booth visits that can be
made in the technology sector. Find the minimum value of
p
for which a student can
expect to get an interview in his/her senior year.
What does this mean, on average,
about the C student in 313?
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 Spring '08
 Milenkovic,O
 Normal Distribution, Probability theory, Maximum likelihood, Bo Schembechler

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