Economic Statistics Exam 2
Last name:
November 3, 2011
First name:
Class time:
SOLUTIONS
PID:
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This exam contains
twelve
short answer questions (worth 6 points each) and
three
long answer questions (worth 10 points each).
Please answer in the space
provided.
In all problems where you need to make a calculation, simplify your
answer as much as possible.
Technique is important, so show your work clearly.
Some PDFs:
Some probabilities:
f
(
x
)
=
1
2
πσ
2
e
−
(
X
−
μ
)
2
2
σ
2
P
[
x
≤
a
]
=
1
−
e
−
λ
a
f
(
x
)
=
1
u
−
P
[
x
]
=
x
e
−
x
!
f
(
x
)
=
e
−
x
P
[
x
]
=
n
!
x
!(
n
−
x
)!
p
x
(1
−
p
)
n
−
x
1.
For a binomial distribution with
p
=
0.7
and
n
=
50
, what is the expected value
of
x
, and what is the variance in
x
?
E
[
x
]
=
n
⋅
p
=
50
⋅
0.7
=
35
Var
(
x
)
=
n
⋅
p
⋅
(1
−
p
)
=
50
⋅
0.7
⋅
0.3
2.
In the entire population,
x
is distributed normally with a mean of 5.28 and a
standard deviation of 8.26. If a researcher calculates the mean of a random
sample of
n
=
25
, then what is the distribution of his/her sample mean,
x
?
x
~
N
(
x
,
x
2
/
n
)
, which is
x
~
N
(5.28,8.26/25)
.
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View Full DocumentEcon 400 Midterm 2, page 2 of 6.
3.
X
~
N
(1,9)
. You collect a sample of
n
=
25
. What is the probability that
X
>
3
?
X
has a mean of 1 and standard deviation of
9 25
=
.
P
[
X
>
3]
=
P
[
Z
>
(3
−
1)/(3/5)]
=
P
[
Z
>
10/3]
=
P
[
Z
>
3.33]
. Depending on the ztable
you use, the answer is either “0.0004” or “less than 0.50000.4990” or
“approximately 0.0000”.
4.
Two random variables,
x
and
y
, have a joint distribution. What is the formula
for calculating the covariance between the random variables?
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 Normal Distribution, Standard Deviation, Variance, Probability theory

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