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Course 4: May 2001
 41 
STOP
1
D
26
A
2
B
27
E
3
C
28
E
4
E
29
D
5
C
30
C
6
C
31
A
7
D
32
A
8
E
33
A
9
D
34
D
10
A
35
E
11
D
36
D
12
E
37
B
13
B
38
B
14
C
39
E
15
A
40
C
16
C
17
E
18
A
19
B
20
E
21
C
22
E
23
B
24
B
25
C
COURSE 4
MAY 2001
MULTIPLECHOICE ANSWER KEY
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Course 4 Exam Solutions
May 2001
Item Number:
1
Key: D
Solution
Because the autocorrelation function is zero starting with lag 2, this must be an MA(1) model.
Then,
22
1
1
1
111
2
1
.
4
,
.
4
.
4
,.
4
.
4
0.
1
q
r
q qqq
q

=
=


=

+=
+
This quadratic equation has two roots, 0.5 and 2.
Because the coefficient’s absolute value must
be less than 1, only 0.5 is acceptable.
C42001A
Item Number:
2
Key: B
Solution
The posterior distribution is
2
/
3
2 4 /3
1
(
2)
2
!3
e
ee
l
ll
l
p


∝∝
which is a gamma distribution
with parameters 3 and 3/4.
The variance is 3(3/4)
2
= 27/16.
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Item Number:
3
Key: C
Solution
( 29 ( 29 ( 29 ( 29 ( 29
( 29 ( 29 ( 29 ( 29 ( 29
22222
2
2
44444
4
4
2
4
1
3
2
3
3
3
4
3
53
2
5
1
3
2
3
3
3
4
3
6.8
5
6.8
1.7
4
ms
m
m
g
s
 + + + +
=
==
===
C42001A
Item Number:
4
Key: E
Solution
The calculations for each possibility are:
Censored at 1
Censored at 2
Censored at 3
Censored at 4
Censored at 5
Time
d
Y
$
S
d
Y
$
S
d
Y
$
S
d
Y
$
S
d
Y
$
S
1
0
5
1
1
5
.80
1
5
.80
1
5
.80
1
5
.80
2
1
4
.75
0
4
.80
1
4
.60
1
4
.60
1
4
.60
3
1
3
.50
1
3
.53
0
3
.60
1
3
.40
1
3
.40
4
1
2
.25
1
2
.27
1
2
.30
0
2
.40
1
2
.20
5
1
1
0
1
1
0
1
1
0
1
1
0
0
1
.20
This result may also be obtained by general reasoning.
If the lapse occurs late, then the “death”
times come earlier, leading to lower survival probabilities.
If the lapse occurs early, then the
“death” times come later, leading to higher survival probabilities.
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Item Number:
5
Key: C
Solution
This is testing
0
45
:
0,
H
bb
==
which is a joint test on several regression coefficients.
The key formula is 5.21 (p.130 of Pindyck and Rubinfeld).
We are given:
R
UR
2
094
=
.
Also, we know:
N
k
=
=
42
5
,
(total number of coefficients to be estimated) and
q
=
2
Using 5.21, we obtain
F
=



=
0915
2
1
42
5
77
.
.
/
.
/
.
b
g
b
g b
g
.