Topic: Sequential Decision trees and Probabilities 17, 11:59pm (Sep...

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Topic: Sequential Decision trees and Probabilities 17, 11:59pm (SeptemberFebruary 3) 1. John Doe, a super-genius student (known also under his nick-name Wile E. Coyote, super-genius) has just graduated from SPEA and found a job that will allow him to purchase a car to finally catch Roadrunner. He can either buy a new car at a cost of $22,000, buy a used car for $12,000 or lease a new car for one year at a cost of $8,500 (assume total cash purchase up front, no financing or monthly payments required). The new car has a 20% chance of a serious break down resulting in a permanent impairment to the trade-in value. The trade-in value for the new car without a serious break down after one year is $18,000 but only $10,000 if the break down occurs. On the other hand, the used car has a 40% chance of suffering a major break down with a $8,000 decrease in the resale value. However, if it does not break down, Wile can sell it to a friend one year from now for $9,000 cash (assume he can also sell it to the friend for $4,000 if the breakdown occurs). Finally, the leased car has a 10% chance of breaking down with a repair cost of only $2,000, and if it doesn’t, Wile will not gain or lose anything by returning the car at the end of a one year lease period. NOTE: For the new and used car purchases all related repair costs resulting from a breakdown have been netted against the trade-in / resale value. a. Construct a decision tree for Wile. (you may want to use MS Word drawing tool or Paint graphical editor in Windows to draw the tree) b. What is the expected value of the new car? c. Whatistheexpectedvalueoftheusedcar? d. Whatistheexpectedvalueofleasingthecar? e. What should Wile E. Coyote do? 2. The SPEA’s administration was concerned about the potential loss that might occur in the event of a power failure. The school estimated that the loss from one of these incidents could be as much as $10 million, including losses due to interrupted student service and potential loss of data collected for years in NSF and DoD sponsored projects. One alternative the school is considering is the installation of an emergency power generator. The cost of the emergency generator is $80,000, and if it is installed, no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 12% chance that a power outage will occur during a year. If there is an outage, there is a .07 probability that the resulting losses will be very large, or approximately $7 million in net aggregated loss. Alternatively, it is estimated that there is a .93 probability of only slight losses of around $1 million. Using decision tree analysis, determine whether the SPEA should have install the new power generator. 3. 20 randomly selected politicians (the U.S. House) were asked about their support on Gun Legislation. Their responses are listed below along with their political affiliation. Show your work. 1 Republican 2 Democratic 3 Republican 4 Republican 5 Democratic 6 Democratic 7 Republican 8 Democratic 9 Democratic 10 Republican 1. Fill out the probability table: Polit.Party Democratic Republican Marginal No 11 Yes 12 No 13 Yes 14 No 15 Yes 16 No 17 Yes 18 Yes 19 Yes 20 Democratic Yes Republican No Democratic Yes Democratic Yes Republican No Republican No Democratic Yes Republican No Democratic No Democratic Yes Support GUN Legislation Yes No Marginal What is the probability that randomly selected politician is 2. a republican P(R)= 3. a Democrat P(D)= 4. a Republican and supporter P(R,S)= 5. a Supporter and Democrat P(S,D)= 6. a politician not supporting the legislation P(notS)= What is the probability to randomly selected politician is 7. a Democrat given the politician is a Supporter of Gun legislation P(D|S)= 8. a Republican given the politician is a Supporter of Gun legislation P(R|S)= (Solve 9-10 use the Bayes theorem: P(A|B) P(B)=P(B|A) P(A) and results obtained in 2. and 3., together with the results obtained in 7. and 8. Above. (see ch.11 and the Handout worked in class week3)) 9. a Supporter of Gun legislation given the politician is a Republican P(S|R)= 10. a Supporter of Gun legislation given the politician is a Democrat P(N|D)=_

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