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IE 523 Probabilistic Analysis
Homework # 3
Due: Thursday, October 22, 17:00.
To be submitted to EA 323.
Question 1:
Suppose that the random variables (X, Y) have the following joint PDF:
(1
),
0
(, )
(
1
)
,
0
0,
/ .
yx
xy
ee
x
y
fxy
e
e
y x
ow
−−
⎧
−<
<
<
∞
⎪
=−
<
<
<
∞
⎨
⎪
⎩
a.
Prove that
,
XY
f
is a bivariate PDF.
b.
Find
{2
,4
}
PX
Y
≤≤
.
c.
Find
2
[
]
EXY X
.
Question 2:
A certain bachelor decides on using the following strategy to find the girl he will marry.
First, he will do a trial date (Date 0) and give a score to this girl.
Then he will keep on selecting new
dates randomly and giving them scores until he finds out a girl who has a higher score than Date 0.
At
this point he will stop dating and marry the girl with the higher score.
Since the dates are selected at
random, the date scores should form a sequence of i.i.d random variables (
S
0
,
S
1
,
S
2
…) with a certain
distribution.
It is reasonable to assume that the scores are continuous and positive random variables.
Let
N
denote the date number of the wife to be.
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 Spring '10
 zeynephuygur

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