11ProbHw8 - IEOR 3658 Probability Prof. Mariana...

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IEOR 3658 Assignment #8 Probability November 2, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #8 – due November 9th, 2011 1. The time Andrew will be at the dentist has an exponential distribution with mean of one hour. He comes to a parking meter which costs $0.5/hour. (Assume he can buy any continuous amount of time he wants, using a smart card). A parking ticket costs $25. If he returns to the car shortly after the meter runs out, the probability of getting a ticket is small. However, if he is gone for a long time after the meter runs out, then the probability of a ticket is high. Let X be the number of hours since the meter ran out and A the event that Andrew gets a ticket, then P ( A | X = x ) = 1 - e - 0 . 5 x . (a) Suppose Andrew puts $ y in the meter, what is the probability that he will get a ticket? (b) To minimize his expected expense, how much money should he put in the meter? 2. (From text) We start with a stick of length
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This note was uploaded on 12/11/2011 for the course IEOR 3658 taught by Professor Olvera during the Fall '08 term at Columbia.

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