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Math 431 Second Evening Exam
Version B
Room B123, 5:00pm  6:00pm, November 19, 2004
M´arton Bal´azs
NAME:
1.
In the post ofce there are two clerks, Mr. A and Mr. B. When I arrive, both oF them have
just started serving a customer, but I am next in line. Mr. A and Mr. B serve customers in
X
and in
Y
minutes, respectively, where
X
and
Y
are two independent exponential random
variables,
X
with parameter 2, and
Y
with parameter 3.
(a)
(15 points) What is the probability that I will have to wait
t
minutes beFore being served,
i.e. the probability oF
{
X > t, Y > t
}
? Show your computation, or explain your answer.
(b)
(15 points) Using your answer in (a), what is the distribution oF my waiting time beFore
being served? What is my expected waiting time?
1
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View Full Document (c)
(20 points) Compute the probability that I will be served by Mr. A, i.e. the probability of
the event
{
X < Y
}
. Show your computation, or explain your answer.
(d)
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This note was uploaded on 08/11/2008 for the course MATH 431 taught by Professor Balazs during the Fall '05 term at Wisconsin.
 Fall '05
 BALAZS
 Math, Probability

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