Econ 375 Study Problems
Burhan Biner
January 25, 2010
You can have a cheat sheet for the midterm exam. Please write whatever you
deem necessary on both sides of an A4 paper. I am going to list a few problems that
might be helpful for the exam.
Mind you, you are responsible for everything
we have done in class and on the homework assignments. Every problem
I solved in class and assigned for homework are good study problems.
You should have a look at the end of chapter problems in the Statistics lecture
notes I posted on the blackboard. Some of the problems I am listing here are for
after the midterm, we won’t be able to get to them before the midterm.
Exercise 1
Solve problems B1, B2, B3, B4, B5, B6, B7, B8, B11, B12, B13 in
Appendix B.
Exercise 2
Solve problems C1, C2, C3, C4, C5, C6, C8, C9 in Appendix C.
Exercise 3
Solve problems 2.2, 2.5, 2.6, 2.7, 2.8 in Chapter 2.
Exercise 4
Explain why the following variables can be thought of as random vari-
able: the gender of the next person you meet, the number of times a computer
crashes, the time it takes to commute to school, whether the computer you are
assigned in the library is new or old, whether it is raining or not.
Exercise 5
Suppose that the random variables
X
and
Y
are independent and you
know their distributions. Explain why knowing the value of
X
tells you nothing
about the value of
Y
.
Exercise 6
An econometrics class has 80 students, and the mean weight is 145
lbs. A random sample of 4 students is selected from the class and their average
weight is calculated. Will the average weight of the students in the sample equal
145 lbs. Why or why not? Use this example to explain why the sample average,
¯
Y
,
is a random variable.
Exercise 7
Let
Y
denote the number of heads that when two coins are tossed.
•
Derive the probability distribution of
Y
.
•
Derive the cumulative probability distribution of
Y
.
•
Derive the mean and variance of
Y
.
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Exercise 8
Suppose
X
is a Bernoulli random variable with
P
(
X
= 1) =
p
.
•
Show
E
(
X
3
) =
p
.
•
Show
E
(
X
k
) =
p
for
k >
0
.
•
Suppose that
p
= 0
.
3
. Compute the mean, variance, skewness and kurtosis of
X
.
Exercise 9
In September, Seattle’s daily high temperature has a mean of
70
F
and
standard deviation of
7
F
. What is the mean, standard deviation and variance in
C
.
Exercise 10
The following table gives the joint probability distribution between
employment status and college graduation among those either employed or looking
for work (unemployed) in the working age U.S. population, based on the 1990 U.S.
Census.
Joint Distribution of Employment Status
and College Graduation in the U.S. Population Aged 25-64, 1990
Unemployed
(
Y
= 0)
Employed
(
Y
= 1)
Total
Non-college grads (
X
= 0
)
0.045
0.709
0.754
College Grads
(
X
= 1)
0.005
0.241
0.246
Total
0.050
0.950
1.00
•
Compute
E
(
Y
)
.
•
The unemployment rate is the fraction of the labor force that is unemployed.

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