Section M
Quiz 3
Version B
ECON 506, Section M
Solution
NAME: ___Ali Toossi_________________
Quiz 3, Version B
November 11 2010
NetID: ______________________________
Total points: 50
I.
(5 points)
Suppose that a company has determined that the number of jobs per week,
N
, varies from week to week and has a Poisson distribution with mean λ. The number of
hours to complete each job Y
i
, is gamma distributed with parameters α and β. The total
time to complete all jobs in a week is
∑
=
=
N
i
i
Y
T
1
. What is E (T  N =
n
) and E (T)? [Use
iterated expectation].
Solution:
∑
∑
∑
=
=
=
=
=
=
=
=
n
i
n
i
i
n
i
i
n
Y
E
Y
E
n
N
T
E
1
1
1
)
(
)
(
)

(
αβ
λαβ
=
=
=
=
=
)
(
)
(
)]

(
[
)
(
n
E
n
E
n
N
T
E
E
T
E
II.
Let
40
2
1
,
,
,
X
X
X
denotes a random sample of size 40 from the uniform distribution
U (0, 1). Suppose
X
is the mean of this sample. Let
30
2
1
,
,
,
Y
Y
Y
denotes a random
sample of size 30 from the standard normal distribution.
(a) (5 points)
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 Fall '08
 Staff
 Normal Distribution, Probability theory, probability density function, Yi, Cumulative distribution function

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