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Unformatted text preview: ing. Let T1 , T2 , T3 , . . . be the arrival times of a Poisson process
with rate , and let U1 , U2 , . . . Un be independent and uniformly distributed on
[0, t]. If we condition on N (t) = n, then the set {T1 , T2 , . . . Tn } has the same
distribution as {U1 , U2 , . . . , Un }. 2.6 Exercises
Exponential distribution 2.1. Suppose that the time to repair a machine is exponentially distributed
random variable with mean 2. (a) What is the probability the repair takes
more than 2 hours. (b) What is the probability that the repair takes more than
5 hours given that it takes more than 3 hours.
2.2. The lifetime of a radio is exponentially distributed with mean 5 years. If
Ted buys a 7 yearold radio, what is the probability it will be working 3 years
later?
2.3. A doctor has appointments at 9 and 9:30. The amount of time each
appointment lasts is exponential with mean 30. What is the expected amount
of time after 9:30 until the second patient has completed his appointment?
2.4. Copy machine 1 is in use now. Machine 2 will be turned on...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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