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THE UNIVERSITY OF CHICAGO
Graduate School of Business
Business 42401, Spring Quarter 2000, Mr. Ruey S. Tsay
Midterm Exam
Notes
:
1. Open book and notes. The exam time is 80 minutes.
2. Write your answers in a bluebook. Mark the solution clearly.
1. Let
Z
= (
Z
1
, Z
2
, Z
3
)
0
be a 3dimensional Gaussian random variable with mean
μ
=
(

3
,
4
,
2)
0
and covariance matrix
Σ
=
1
0

1
0
2
0

1
0
2
.
Consider the following questions or statements. If the statement is true, brieFy justify
it such as citing a result from the textbook. If the statement is false, please explain
why.
(a)
Z
1
+
Z
3
is independent of
Z
2
.
(b) (
Z
1
, Z
3
)
0
is independent of
Z
2
.
(c) Consider the simple linear regression model
Z
1
=
β
0
+
β
1
Z
3
+
²,
where
E
(
²
) = 0 and
²
is uncorrelated with
Z
3
. ±ind the values of
β
0
and
β
1
.
(d) What is the conditional distribution of
Z
1
given that
Z
3
= 3?
(e)
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