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ECON 506M
Quiz2A, October 4, 2007
NAME:
I.
Let Y be a random variable distributed as following:
Y
P(Y)
1
a
2
b
Assuming E(Y) = 1.7 find the values of
a
&
b
(8 points)
Here you have to solve a system of equations (2 equations and 2 unknowns, a and b).
3
.
7
.
7
.
1
*
2
1
7
.
1
)
(
*
2
*
1
1
=
⇒
=
⇒
=
+

⇒
=
=
+
=
+
a
b
b
b
Y
E
b
a
b
a
For the rest of this question, assume
a
= 0.2 and
b
= 0.8.
Find the variance (
8 points)
For the variance we need to get the first and second moments.
16
.
0
9
.
1
7
.
3
)
(
4
.
3
2
*
8
.
1
*
2
.
)
(
8
.
1
2
*
8
.
1
*
2
.
)
(
2
2
2
2
=

=
⇒
=
+
=
=
+
=
Y
V
Y
E
Y
E
Find E(
Y
3
)
(6 points)
8
.
1
2
/
3
*
8
.
3
*
2
.
)
/
3
(
=
+
=
Y
E
II.
A politician believes that 25% of all macroeconomist in senior position would
strongly support a proposal he wishes to advance. Suppose that this belief is correct. 5
senior macroeconomists are approached at random.
What is the probability that at least one of the five would strongly support the proposal?
(6
points)
In this case we need to use a binomial distribution, since n=5 is fixed. Suppose that
we consider a success when a macroeconomist support the proposal (then p=prob of
success is =.25). Define Y = number of macro economists that support the proposal.
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 Fall '08
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