M362K
Sample Test 3A
Dr. Gary Berg
All problems are worth ten points. Do ten of the twelve problems. Clearly mark the problems to be
omitted.
Show your work.
1)
The joint density function of
X
and
Y
is given by
f
(
x
,
y
)
=
2
e
−
x
e
−
2
y
for positive
x
and
y
and is zero
otherwise. Find
P
(
X
<
Y
)
.
2)
Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white and 8 red
balls. Let
X
i
equal 1 if the
i
th ball is white, and is 0 otherwise. Give the joint probability mass function of
X
1
,
X
2
.
3)
If
X
and
Y
are independent continuous positive random variables, express the density function of
Z
=
X
/
Y
in terms of the density functions of
X
and
Y
.
4)
A television store owner figures that 45 percent of the customers entering his store will purchase
an ordinary television set, 15 percent will purchase a plasma television set, and 40 percent will just be
browsing. If 5 customers enter the store on a given day, what is the probability that he will sell 2 ordinary
sets and 1 plasma set on that day?
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 Spring '11
 Berg
 Probability, Variance, Probability theory, probability density function, joint density function

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