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Answers to additional paper and pencil Questions Please bring any errors to my attention Fall 2004
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Chapter 4 Question 1 a) PA B PA PB PB ∪= + =+ = b g b g b g b g bg .. . 65 0 1 2) + = b g b g b g b g . . 5 2 3) + = b g b g b g b g . . 4 16666 Question 2 Clean (.80) Dirty (.20) “Dirty” (.90) “Dirty” (.05) “Clean” (.10) “Clean” (.95) .76 .04 .02 .18 .76 .02 “Clean” (.78) .04 .18 “Dirty” (.22) Clean (.974) Dirty (.818) Clean (.182) Dirty (.026)
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Question 3 a) () .49 PG W N ∪∪ = b) .40 PG W ∪= c) .16 .40 .40 PNG W = d) .07 c PG N ∩= e) .07 .75 .0933 c PGN == Question 4 I call this my “Mickey Mouse” question. Look at the Venn Diagram. ( ) () ( ) ( ) ()() .0002 .0008 PA B PAPBA PAPB PA C PAPCA PAPC = = = = Ans: .069 Wheaties Gatorade Nikes .02 .03 .06 .08 .04 .17 .09 .51 A B C .0008 .0002 .019 .0098 .0392 .931
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Chapter 5 Question 1 a) µ = 3 and σ = 26 . b) Expected wealth is you take the offer is $250,000; expected wealth if you reject it is $300,000. If you care only about expected wealth, you reject it. c) Expected utility if you take the offer is EU b g b g =∗− = 10 2 5 2 5 18 75 2 .. . . If you reject it and take the auction, your expected utility is Ex bg ch b g b g =− = + =∗−+ = 10 10 10 3 9 2 6 18 4 22 2 µµσ () . Therefore you are better off accepting the buyout offer. d) This person seems to be risk averse. They turn down an alternative with a bigger expected payoff in favor of one that has a smaller payoff but no risk. Question 2 a) µσ == 11 2 , b) y a bx x ab b yx =+ = + =+ = = 100000 7500 107500 7500 56 250 000 2 2 µµ σσ ,, Question 3 Ans: .3105 - .1628 = .1477 Question 4 a) f f f 0 2 0 19 8 1 1 2 1 19 1 8 2 2 2 19 0 1 02 20 bgb g b gb g b g b g b g = F H G I K J = = F H G I K J = = F H G I K J = . . .
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b) f f f 0 2 0 18 2 20 2 153 190 8053 1 2 1 18 1 20 2 36 190 1894 2 2 2 18 0 20 2 1 190 0053 b g bg = F H G I K J F H G I K J F H G I K J == = F H G I K J F H G I K J F H G I K J = F H G I K J F H G I K J F H G I K J . . . In part b the draws are not even approximately independent; getting a defective on the first draw lowers the chance of getting a second, while getting a non-defective on the first draw also lowers the chance of getting a second non-defective. Question 5 fff e e e 012 74 1 2 0006 0045 0167 0218 2 b g b g b g ++ + + = . . . . . ! ... . Question 6 a) f 3 5 3 29 2 34 5 4060 278256 0145909 b g = F H G I K J F H G I K J F H G I K J . 2) f 4 5 4 29 1 34 5 145 278256 000521103 b g = F H G I K J F H G I K J F H G I K J 3) f 5 5 5 29 0 34 5 1 278256 b g = F H G I K J F H G I K J F H G I K J = 4) The calculations below show the expected value of the ticket is about $0.484, so that the average loss on each ticket is $0.516.
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x f(x) xf(x) 0 0.984884 0.000000 5 0.014591 0.072955 100 0.000521 0.052110 100,000 0.000004 0.359400 0.484460 Question 7 Using the binomial, the chance of no blacks is f 0 50 0 01 99 6050 05 0 bg b gb g = F H G I K J = .. . , and the chance of at least one is 1 0 1 6050 3950 = − = f b g . Using the poisson approximation, with µ = = np .50, the probability of no blacks is f e 0 5 0! 6065 0 5 b g == . . . , and the probability of at least one is 1 0 1 6065 3935 = = f b g . Question 8 a) First you need to show that xy = = 19 7 , . Then we know that σµ xy x y x y f x y =− +− + −−+ −− = b g di b g b g b g b g b g b g b g b g b g b g b g b g b g , ...
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This note was uploaded on 03/01/2012 for the course ECON 371 taught by Professor Staff during the Spring '08 term at UVA.

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answers - Answers to additional paper and pencil Questions...

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