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)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Normal Distribution, Probability theory, probability density function, Yi, Cumulative distribution function

Click to edit the document details