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IEOR 3658
Assignment #8
Probability
November 2, 2011
Prof. Mariana OlveraCravioto
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.
 Fall '08
 Olvera

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