University of Illinois
Fall 2009
ECE 313:
Hour Exam II
Monday November 16, 2009
7:00 p.m. — 8:00 p.m.
100 Materials Science and Engineering Building
1.
[15 points]
Messages can be transmitted between ChampaignUrbana and Springfield either
directly or via Decatur on communication links whose capacities are indicated on the diagram
shown below. Assume that the three links fail independently with equal probability
1
2
. Let
X
denote the communication capacity between ChampaignUrbana and Springfield.
40
Springfield
ChampaignUrbana
Decatur
200
100
(a)
[5 points]
What values can
X
take on?
(b)
[10 points]
Find the expected value of
X
.
2.
[10 points]
Let
X
denote a
Gaussian
random variable with mean 2 and variance 25.
Use the table of values of the unit Gaussian CDF Φ(
·
) on the last page of this exam booklet
to find the numerical value of
P
{
X

4

>
3
}
.
3.
[15 points]
Let
X
denote a continuous random variable with zero mean and variance 1, that
is,
E
[
X
] = 0 and
var
(
X
) = 1.
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 Spring '10
 S
 Probability theory, Decatur

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