Stat 351 Fall 2007
Assignment #7
This assignment is due at the beginning of class on Friday, November 9, 2007. You must submit
solutions to all problems. As indicated on the course outline, solutions will be graded for both
content and clarity of exposition. The solutions that you submit must be neat and orderly. Do
not crowd your work or write in multiple columns. Your assignment must be stapled and problem
numbers clearly labelled.
1.
Suppose that
X
1
and
X
2
are independent
N
(0
,
1) random variables. Set
Y
1
=
X
1

3
X
2
+ 2
and
Y
2
= 2
X
1

X
2

1.
(a)
Determine the distributions of
Y
1
and
Y
2
.
(b)
Determine the distribution of
Y
= (
Y
1
,Y
2
)
0
.
2.
Let
X
have a threedimensional normal distribution with mean vector
μ
and covariance
matrix Λ given by
μ
=
3
4

3
and Λ =
2
1
3
1
4

2
3

2
8
,
respectively. If
Y
1
=
X
1
+
X
3
and
Y
2
= 2
X
2
, determine the distribution of
Y
= (
Y
1
,Y
2
)
0
.
3.
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 Fall '08
 MichaelKozdron
 Normal Distribution, Probability, Standard Deviation, Variance, Probability theory, probability density function, µ

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