06 STAT HWA a - Dr. V.R. Bencivenga Economics 329 PRACTICE...

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Unformatted text preview: Dr. V.R. Bencivenga Economics 329 PRACTICE HOMEWORK #6B: CONTINUOUS RANDOM VARIABLES ANSWERS 1.a. x f 1/60 0 20 60 3 2 60 40 60 30 60 10 25 55 60 1 5 15 60 1 55 X 25 X P 15 X 5 X P b. 7 . 60 / 50 60 / 35 10 60 60 1 25 55 60 1 5 10 60 1 10 X P 55 X 25 X P 15 X 10 X P c. The garage in City A gets cars that break down in the interval 10 x ; the probability of this is 6 1 10 60 1 10 x P , so this garage earns 1/6 of your revenue. The garage in City B gets cars that break down in the interval 40 x 10 ; the probability of this is 5 . 60 30 10 40 60 1 40 x 10 P , so this garage earns half of your revenue. Therefore, the garage in city C, which gets cars that break down in the interval 60 x 40 , earns 1/3 of your revenue (the probability of getting towed to the garage in City C is 1/3). d. D = distance towed 60 40 X 40 20 X 20 10 X 10 X dx x f x 60 dx x f 20 x dx x f x 20 dx x f x D E 60 40 2 60 40 40 20 40 20 2 20 10 2 20 10 10 2 x 2 1 x 60 x 20 x 2 1 x 2 1 x 20 x 2 1 60 1 2 2 2 2 2 2 2 2 40 60 2 1 40 60 60 20 40 20 20 40 2 1 10 20 2 1 10 20 20 10 2 1 60 1 800 1800 2400 3600 400 800 200 800 50 200 200 400 50 60 1 3 1 8 500 60 1 800 1800 2400 3600 400 800 200 800 50 200 200 400 50 60 1 Expected cost is 2 times expected distance, since the cost is $1 per mile, and the tow truck must make a round trip. 2 e. The maximum distance a tow truck from a garage must drive to any breakdown must be the same in both directions, and that maximum distance must be the same for all three garages, as depicted in the following diagram: x f 1/60 0 10 20 30 40 50 60 Locate the stations at 10, 30, and 50. The first station will tow cars that break down from 0 to 20 miles; the second station will tow cars that break down from 20 to 40 miles, and the third station will tow cars that break down from 40 to 60 miles....
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06 STAT HWA a - Dr. V.R. Bencivenga Economics 329 PRACTICE...

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