139Spring 2010 FINAL
Name:
.............................................
NetID
............
DO NOT TURN OVER UNTIL TOLD TO DO SO
Notes:
1. Use a calculator where necessary.
2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.
3. If you want to make any additional assumptions to simplify a problem, please state them clearly.
4.
Keep verbal answers concise
(no more than 4 sentences, and bullet points are °ne).
Guide:
There are 119 points and you have 150 minutes.
Problems 1 and 2 cover material in the °rst part of the course, and problem 2 requires proofs.
Background:
Problems 1, 3, 4, 5 and 6 are motivated by the economics of the retail gasoline
industry.
This industry has undergone a lot of structural change in many states due to the entry of
large retailers (such as Walmart/Sam±s Club) and Costco into providing gasoline.
In response some
states and governments have enacted laws designed to protect small gasoline retailers.
One useful
piece of terminology : the
markup
is the di/erence between the retail price paid by consumers and
the wholesale cost of gasoline in a particular market, excluding taxes.
For example, if the retail price
(excluding taxes) is $2.00 per gallon and the wholesale price is $1.90 per gallon then the markup would
be 10 cents.
For the purpose of this exam, forget about taxes.
Oil
majors
are °rms such as Exxon,
BP and Shell.
Good Luck and Enjoy the Summer.
1
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1.
The data contains information on whether a gas station is owned by one of the major oil
companies (otherwise it is an independent) and whether it o/ers diesel as well as regular gasoline.
The following table shows the division of stations in the sample:
Major
Independent
Diesel
500
200
No Diesel
400
350
For all of the calculations below, show your working.
You can leave your answers as fractions.
(a) (2 points) If a station is selected at random from this sample, what is the probability that it is
an independent station that o/ers diesel?
Solution: the joint probability is
200
500+400+200+350
=
4
29
(b) (3 points) If a station is selected at random from this sample, what is the probability that it is
owned by a major?
Solution:
500+400
500+400+200+350
=
18
29
(c) (2 points) If an independent station is selected at random from this sample, what is the proba
bility that it o/ers diesel?
Solution: conditional probability:
200
200+350
=
4
11
(d) (6 points) You are also interested in whether stations have convenience stores.
Suppose that
in the population (i.e., not just the sample), the probability that a station o/ers diesel is 0.6, the
probability that a station has a convenience store is 0.3 and the probability that a station both o/ers
diesel and has a convenience store is 0.18.
Can you conclude that the characteristics of having a
convenience store and o/er diesel are
independent
?
Clearly state the condition for independence,
and explain your working.
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 Spring '08
 ALESSANDROTAROZZI
 Econometrics, Gasoline, Bigbox store, Filling station, big box

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