Ec 120A OLD EXAMS (Foster)
I DO NOT DISCUSS OLD EXAMS!
These are provided to you to give you some idea of the level of
questions on my midterms and finals.
If having these problems to look at helps you, then good.
If
not, feel free to ignore them.
Midterm Exam #1 – Fall 1980
Problem 1
Rodney Random has just taken a job with Fasbux Financial consultants.
His first task
is to evaluate two bonds (A and B) with regard to “expected rate of return” and “risk of
default.”
He obtains 6 quarterly observations on the rates of return for each bond,
measured as percents per year (see Table A).
Let the sample mean
R
measure bond
expected return, and sample variance s
2
measure bond risk.
Most Fasbux clients want
high rates of return and low risk.
How will Rodney advise these clients with regard to
Bonds A and B?
(Show or summarize your calculations which you use to support your
opinion.)
•
24
%
7
2
%
5
2
2
=
=
=
=
b
b
a
a
s
R
s
R
Problem 2
Pretend that the 12 observations in Table A are a single sample of n = 12 measurements of rate of
return for one bond.
A)
Prepare a cell frequency table for the data R
i
, i = 1…12.
Use Sturgis’ Rule and round down
.
Let your first interval be 0 – 3.99 with midpoint 2.
Fill in Table B, then sketch the histogram of
these data.
B)
Calculate the average rate of return for the 12 observations, using the appropriate formula for
data grouped into cells (intervals).
•
33
.
6
=
R
Problem 3
Table A
A
B
4
6
3
5
5
7
1
10
8
2
14
7
Table B
Interval
M
j
f
j
f
j
/n
0 – 3.99
2
3
4 – 7.99
6
8 – 11.99
10
0.167
12 –
15.99
14
0
4
8
12
16
r
f
f/n
Fig. A
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Ec 120A (Foster)
OLD EXAMS
p. 2
In the Venn diagram at right, S is the universe (sample
space of an experiment), and event D
⊂
C.
A)
Do events A, B, C, D and E partition of S?
No
B)
What is Pr(BA)?
0
C)
What is Pr(CD)?
D)
What is Pr(~BE)?
E)
Shade the event ~D
∩
C.
Problem 4
The EPA conducts an experiment in which 40
automobiles of varying horsepower are tested for exhaust emission standards violations.
The cars
are grouped into 3 horsepower categories:
compact, midsize, and muscle cars.
There are 20
compact, 15 midsize, and 5 muscle cars in the sample.
The tests show that 1/4 of compacts, 1/3 of
midsize, and 4/5 of muscle cars fail the
tests.
A)
Fill in the empty cells in Table B
with the correct number of cars.
Cell
e
6
has been filled in for illustration.
B)
The experiment consists of drawing a
car from a set of 40 cars and observing its horsepower category and its test performance.
There
are obviously 6 possible outcomes e
1
… e
6
.
What is Pr(e
1
)?
0.125
C)
Event F is “Car fails test.”
What is Pr(F)?
0.35
D)
What is Pr(C2
∩
F)?
0.125
What is Pr(C2
∪
C3)?
0.50
E)
The Bayesian question.
One of the cars tested by the EPA is a stillsecret Fosterfire Phaeton
ZTX Sport Megahummer.
You learn that the Fosterfire vehicle failed the test.
What is the
probability that the Fosterfire is a muscle car?
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 Spring '09
 Foster
 Normal Distribution, Variance, Probability theory, probability density function, 120A (Foster)

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