Spring 2011 OR3510/5510
Problem Set 6
Due Monday March 14.
Reading: We are working on the Poisson process and variants in Chapter 5.
(1) One hundred items are simultaneously put on a life test.
Suppose the life times of the
individual items are independent exponential random variables with mean 200 hours. The
test will end when there have been a total of 5 failures. If
T
is the time at which the test
ends, nd
E
(
T
) and Var(
T
)
.
(2) Traffic on Snyder Hill Road follows a Poisson process with rate 2/3’s of a vehicle per minute.
10% of the vehicles are trucks and the other 90% are cars.
(a) What is the probability at least one truck passes in an hour?
(b) Given that 10 trucks have passed by in an hour, what is the expected number of vehicles
that have passed by?
(c) Given 50 vehicles have passed by in an hour, what is the probability there were exactly
5 trucks and 45 cars.
(3) Customers arrive at a twoserver service station according to a Poisson process with rate
λ
.
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 Spring '09
 RESNIK
 Probability theory, Exponential distribution, Harry, Poisson process

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