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Department of Economics
Fall 2007
University of California
Prof. Woroch
Economics 140:
Problem Set 1 Answer Sheet
Instructions:
Include names and SIDs of the members of your study group and the name of the
single GSI for all of you.
When asked to solve a question using Excel, write the final answer on
your answer sheet and also attach a printout of the relevant portion of the Excel file.
Include all
intermediate steps and indicate clearly the final solution (
i.e.
different color, box, etc.). Staple your
answer sheets—otherwise it will not be accepted.
1.
A damaged coin comes up “heads” with probability p = 3/5 and “tails” with probability 1 – p =
2/5.
Suppose this coin is tossed twice. Let M denote the number of heads realized by the two
flips.
a)
List all possible outcomes for M and the associated probability of each one.
b)
Using Excel, generate 50 trials of this simple experiment (i.e., two flips of the damaged
coin).
[Hint: used the =RAND() function in Excel.]
c)
Using the data you generated, use Excel to graph the “probability density function” (p.d.f.)
for this experiment and the corresponding “cumulative distribution function” (c.d.f.), placing
the values of M on the xaxis and probability values on the yaxis.
d)
Compute the sample mean and sample standard deviation of your synthesized data, and
compare to the population mean and standard deviation of the random variable M.
e)
Given your synthesized data, what are the population and sample values for the probabilities
of the following outcomes?
i)
Pr( M = 0)
ii)
Pr( M = 0 or M = 1)
iii)
Pr( M = 1 or M
≠
2)
ANSWER:
a)
M
0
1
2
Pr(M)
4/25
12/25
9/25
b) See Excel answer sheet.
c) See Excel answer sheet
d) The value in sample changes depending on the random number. See excel answer sheet.
Population
Sample
E(M)
1.2
1.26
Std Dev(M)
0.48
0.69
e)
Population
Sample
Pr(M = 0)
4/25 = 0.16
0.22
Pr(M = 0 or M = 1)
16/25 = 0.64
0.6
Pr(M = 1 or M
≠
2)
16/25
0.6
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2.
Download the Excel spreadsheet file called
PS1data.xls
from the Resources section of bSpace.
It contains a dataset with 261 observations. The variables are defined as:
FEMALE:
1 if the individual is female and 0 if the individual is male.
AGE:
Age of the individual.
COLLEGE:
1 if the individual has a college degree, 0 otherwise.
YEAR:
two years, 1992 and 1998.
a)
Use Excel to complete the following table:
1992
1998
Total
Males
Females
Total
Observations
Average Age
Median Age
Std Dev of Age
% College
% College & Age>30
b)
Use Excel to compute the sample covariance and sample correlation between FEMALE and
COLLEGE for each of the two years.
ANSWER:
The values for the missing statistics are computed in the PS1 Excel answer sheet and
reported below.
Look at the cell contents to see the formula.
a)
b) Year 1992: Corr(Female,College) = 0.084
Cov(Female,College)
= 0.0209
Year 1998: Corr(Female, College) =  0.04
Cov(Female,College) =  0.009
3.
In 1998, the campus placement office of a large, public university conducted a survey of starting
salaries of graduating economics majors.
With the help of the registrar, they were able to
anonymously match the reported salaries of 108 graduates with their cumulative GPA during
their undergrad career.
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 Fall '08
 DUNCAN
 Economics

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