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University of Illinois
Fall 2009
ECE 313:
Problem Set 14
Conditional Distributions; Covariance and Correlation
Due:
Wednesday December 9 at 4 p.m.
Reading:
Ross, Chapter 7, Sections 15; Chapter 8, Sections 14
Powerpoint Lecture Slides, Sets 3538
Noncredit exercises:
Ross Chapter 7: Problems 1, 16, 26, 30 33, 34, 38;
Theoretical Exercises: 1, 2, 17, 22, 23, 40
Chapter 8: problems 19, 15.
Reminder:
Due date for homework is Wednesdays at 4 p.m. again
1.
[Is gambling any good?]
John is vacationing in Monte Carlo. Each evening the amount of money he takes to the casino is a
random variable
X
with pdf
f
X
(
u
) =
±
Cu
0
< u
≤
$100
0
else
.
At the end of each night, the amount
Y
he returns with is uniformly distributed between 0 and twice
the amount he came to the casino with.
(a) Find the value of the constant
C
.
(b) For ﬁxed
α
, 0
≤
α
≤
$100, what is
f
Y

X
(
v

α
), the conditional pdf of
Y
given that
X
=
α
?
(c) If John goes to the casino with
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