MA540
Page  1
Homework 5
1)
Problem 2 Page 365
A fair die is tossed twice. The sum of the outcomes is denoted by
X
and the largest value by
Y
.
(a)
Calculate the joint probability mass function of
X
and
Y
;
(b)
Find the marginal probability mass function of
X
and
Y
;
(c)
Find
.
Solution:
(a) and (b)
, the joint probability mass function of
X
and
Y
, and
, the
marginal probability mass functions of
X
and
Y
are given by the following table.
1
2
3
4
5
6
2
1/36
0
0
0
0
0
1/36
3
0
2/36
0
0
0
0
2/36
4
0
1/36
2/36
0
0
0
3/36
5
0
0
2/36
2/36
0
0
4/36
6
0
0
1/36
2/36
2/36
0
5/36
7
0
0
0
2/36
2/36
2/36
6/36
8
0
0
0
1/36
2/36
2/36
5/36
9
0
0
0
0
2/36
2/36
4/36
10
0
0
0
0
1/36
2/36
3/36
11
0
0
0
0
0
2/36
2/36
12
0
0
0
0
0
1/36
1/36
1/36
3/36
5/36
7/36
9/36
11/36
(c)
,
2)
Problem 11 Page 366
Let the joint probability distribution function of the lifetimes of two brands of lightbulb be given
by
Find the probability that one lightbulb lasts more than twice as long as the other.
Solution:
, the joint probability density function of
X
and
Y
is given by
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MA540
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Therefore, by symmetry,
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 Spring '10
 prasad
 Probability, probability density function

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