Introduction to Econometrics
Professor Alexei Onastki
Problem Set 1 – September 23
Problem 1) [
Stock and Watson 2.1
]
(a) Probability distribution function for
Y
Outcome
(number of heads)
Y
=
0
Y
=
1
Y
=
2
probability
0.25
0.50
0.25
(b) Cumulative probability distribution function for
Y
Outcome
(number of heads)
Y
<
0
0
≤
Y
<
1
1
≤
Y
<
2
Y
≥
2
Probability
0
0.25
0.75
1.0
(c)
= ( )
(0
0.25)
(1
0.50)
(2
0.25)
1.00
Y
E Y
μ
=
×
+
×
+
×
=
Using Key Concept 2.3:
and
2
2
var( )
(
)
[
( )] ,
Y
E Y
E Y
=
−
+
×
+
×
2
2
(1
0.50)
(2
0.25)
=
×
=
2
2
(
)
(0
0.25)
1.50
E Y
so that
2
2
2
var( )
(
)
[
( )]
1.50
(1.00)
0.50.
Y
E Y
E Y
=
−
=
−
=
Problem 2) [
Stock and Watson 2.6
]
The table shows that
Pr(
0,
0)
0 045,
X
Y
=
=
=
.
Pr(
0,
1)
0 709,
X
Y
=
=
=
.
=
=
=
.
=
=
=
.
Pr(
1,
0)
0 005,
X
Y
Pr(
1,
1)
0 241,
X
Y
Pr(
0)
0 754,
X
=
=
.
=
=
.
1)
0 246,
Pr(
X
=
=
.
Pr(
0)
0
Y
050,
=
=
.
Pr(
1)
0 950.
Y
(a)
=
=
×
=
+
×
=
=
× .
+
× .
=
.
.
(
)
0
Pr(
0)
1
Pr(
1)
0
0 050
1
0 950
0 950
Y
E Y
Y
Y
μ

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