Econometrics Exam 0
By writing your PID below, you are indicating
Sept. 5, 2008
your intention to abide by the honor pledge:
PID:
This exam consists of
ten
short questions
(
worth four points apiece
)
and
three
long
questions
(
worth twelve points each
)
, for a total of 76 points.
You have 50 minutes
to answer all completely and clearly in the space provided.
For better and for worse,
I am grading you primarily on technique and secondarily on correct answers.
Short Questions
1. Suppose that
X
has a mean of
5
, and variance of
9
;
Y
has a mean of
7
, and
variance of
16
; the two random variables are independent.
If you created
Z
=
2
X
!
Y
, what would be
E
[
Z
]
and
Var
(
Z
)
?
E
[
Z
]
=
E
[2
X
!
Y
]
=
E
[2
X
]
!
E
[
Y
]
=
2
E
[
X
]
!
E
[
Y
]
=
2
"
5
!
7
Var
(
Z
)
=
Var
(2
X
!
Y
)
=
Var
(2
X
)
+
Var
(
!
Y
)
+
2
Cov
(2
X
,
!
Y
)
=
(2)
2
Var
(
X
)
+
(
!
1)
2
Var
(
Y
)
+
2(2)(
!
1)
Cov
(
X
,
Y
)
=
4
"
9
+
1
"
16
!
4
"
0
2. Given three matrices
A
,
B
, and
C
, rewrite the expression
(
A
+
BC
!
)
without
parentheses.
(
A
+
BC
!
)
=
(
A
!
)
+
(
BC
!
)
=
!
A
+
!
C
!
B
3.
What is the difference between “
Var
(
X
)
” and “
V
ˆ
ar
(
X
)
”?
“
Var
(
X
)
” refers to the true variance in
X
in the population; “
V
ˆ
ar
(
X
)
is the
variance that the researcher calculates for his sample of the population.
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 Fall '08
 Staff
 Econometrics, Variance, var, Yi

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