Economics 120A
Name:
_________________________
Professor Yongil Jeon
Summer 2006
Student ID#: _________________________
Answer to Homework #2 – Summer 2006
(Answer to Final Exam, Summer 2005)
Answer all questions on separate paper. This problem set should be handed in to Professor Jeon at
the beginning of your review session on Tuesday, August 1, 2006.
Problem sets may not be
handed in once solutions have been distributed.
Please write down your name and PID clearly.
Good luck!
1a)
(3 points)
The Student
t
distribution is
a.
the distribution of the sum of
m
squared independent standard normal
random variables.
b.
the distribution of a random variable with a chisquared distribution with
m
degrees of freedom, divided by
m
.
c.
always well approximated by the standard normal distribution.
d.
the distribution of the ratio of a standard normal random variable, divided
by the square root of an independently distributed chisquared random
variable with
m
degrees of freedom divided by
m
.
Answer
: d
1b)
(3 points)
When there are
∞
degrees of freedom (that is, with a large sample), the
t
∞
distribution
a. can no longer be calculated.
b. equals the standard normal distribution.
c. has a bell shape similar to that of the normal distribution, but with “fatter”
tails.
d. equals the
2
χ
∞
distribution.
Answer
: b
1c)
(3 points)
The central limit theorem
a. states conditions under which a variable involving the sum of
1
,...,
n
YY
i.i.d. variables becomes the standard normal distribution.
b. postulates that the sample mean
Y
is a consistent estimator of the
population mean
Y
µ
.
c. only holds in the presence of the law of large numbers.
d. states conditions under which a variable involving the sum of
1
,...,
n
i.i.d. variables becomes the Student
t
distribution.
Answer
: a
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HOMEWORK #2, ECON 120A, Summer 2006
1d)
(3 points)
The sample average is a random variable and
a.
is a single number and as a result cannot have a distribution.
b.
has a probability distribution called its sampling distribution.
c.
has a probability distribution called the standard normal distribution.
d.
has a probability distribution that is the same as for the
1
,...,
n
YY
i.i.d.
variables.
Answer
: b
1e)
(3 points)
An estimator ˆ
Y
µ
of the population value
Y
is more efficient when
compared to another estimator
Y
%
, if
a.
E
( ˆ
Y
)
>
E
(
Y
%
).
b.
it has a smaller variance.
c.
its c.d.f. is flatter than that of the other estimator.
d.
both estimators are unbiased, and var( ˆ
Y
) < var(
Y
%
).
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 Summer '08
 Jeyeon
 Economics, Normal Distribution, Variance, ECON 120A

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