University of Illinois
Fall 2009
ECE 313:
Problem Set 12
Joint Distributions of Random Variables
Due:
Wednesday November 18 at 4 p.m.
Reading:
Ross, Chapter 6, Sections 14; Powerpoint Lecture Slides, Sets 3034
Noncredit Exercises:
Chapter 6:
Problems 13, 9, 10, 13, 15, 1923, 4042;
Theoretical Exercises 4, 6; SelfTest Problems 3, 5, 6, 7
Reminder:
Hour Exam II on Monday November 16, 7:00 p.m. – 8:00 p.m., 100 MSEB
Coverage of material is Problem Sets 611
1.
[Joint pmfs]
The joint pmf
p
X
,
Y
(
u, v
) of
X
and
Y
is shown in the table below.
u
→
v
↓
0
1
3
5
4
0
1/12
1/6
1/12
3
1/6
1/12
0
1/12
1
1/12
1/6
1/12
0
(a) Find the marginal pmfs
p
X
(
u
) and
p
Y
(
v
).
(b) Are
X
and
Y
independent random variables?
(c) Find
P
{
X
≤
Y
}
and
P
{
X
+
Y
≤
4
}
.
(d) Find
p
X

Y
(
u

3),
E
[
X

Y
= 3] and
var
(
X

Y
= 3).
2.
[Drill problem on jointly continuous random variables I]
Ross, Problem 6.8, page 287 (Problem 8 on page 313 of the 7th edition)
The joint pdf of
X
and
Y
is given by
f
(
u, v
) =
c
(
v
2

u
2
) exp(

v
)
,

v
≤
u
≤
v,
0
< v <
∞
.
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 Spring '10
 S
 Probability distribution, Probability theory, probability density function

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