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CEE 3040
Fall 2008
Section #2 solutions
1. Devore 5
th
Edition, Section 3.2 #12 on pp. 108
Let
X
= the number of tires on a randomly selected automobile
that are under inflated
a.) Which of the following three
p
(
x
) functions is a legitimate pmf for
X
?
Why are the other two not allowed?
x
0
1
2
3
4
p(x)
0.3
0.2
0.1
0.05
0.05
p(x)
0.4
0.1
0.1
0.1
0.3
p(x)
0.4
0.1
0.2
0.1
0.3
Answer:
The second pmf is the only legitimate pmf
b.) For the legitimate pmf of part (a), compute:
P(2
≤
X
≤
4)
Answer:
0.5
P(
X
≤
2)
Answer:
0.6
P(
X
≠
0)
Answer:
0.6
c.) Suppose:
p
(
x
) =
c
⋅
(5
x
)
for
x
= 0, 1, …, 4
What is the value of
c
?
[
Hint
:
Σ
p
(
x
) = 1]
Answer:
c = 1/15
Counting Problems:
1.
A party has 50 persons. 45 of them are boys. 5 are girls. If we select randomly 6 people,
a.) What is the probability to have exactly 1 girl?
Answer :
Pr[Select exactly 1 girl] = 0.384
b.) To have at least 2 girls?
Answer :
Pr[Select at least 2 girls] = 0.103
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View Full Document CEE 3040
Fall 2008
2.
There are 20 people at a party.
a.) If there are 10 men and 10 women, how many pairs (men with women) are there?
Answer:
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This note was uploaded on 10/13/2010 for the course CEE 3040 at Cornell University (Engineering School).
 '08
 Stedinger

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