Finalwsol2010 - 139-Spring 2010

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Unformatted text preview: 139-Spring 2010 FINALName:.............................................NetID ............DO NOT TURN OVER UNTIL TOLD TO DO SONotes: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 gasolineindustry. This industry has undergone a lot of structural change in many states due to the entry oflarge retailers (such as Walmart/Sams Club) and Costco into providing gasoline. In response somestates and governments have enacted laws designed to protect small gasoline retailers.One usefulpiece of terminology : themark-upis the dierence between the retail price paid by consumers andthe 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 mark-up wouldbe 10 cents. For the purpose of this exam, forget about taxes. Oilmajorsare &rms such as Exxon,BP and Shell.Good Luck and Enjoy the Summer.11. The data contains information on whether a gas station is owned by one of the major oilcompanies (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:MajorIndependentDiesel500200No Diesel400350For 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 isan independent station that o/ers diesel?Solution: the joint probability is200500+400+200+350=429(b) (3 points) If a station is selected at random from this sample, what is the probability that it isowned by a major?Solution:500+400500+400+200+350=1829(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:200200+350=411(d) (6 points) You are also interested in whether stations have convenience stores. Suppose thatin the population (i.e., not just the sample), the probability that a station o/ers diesel is 0.6, theprobability that a station has a convenience store is 0.3 and the probability that a station both o/ersdiesel and has a convenience store is 0.18.Can you conclude that the characteristics of having aconvenience store and o/er diesel areindependent? Clearly state the condition for independence,and explain your working....
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This note was uploaded on 08/02/2011 for the course ECON 139 taught by Professor Alessandrotarozzi during the Spring '08 term at Duke.

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Finalwsol2010 - 139-Spring 2010

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