4.14
Problems
161
the gas station, what is the probability that a waiting line will occur at the
station?
4.38
The number of traffic tickets that a certain traffic officer gives out on any
day has been shown to have a Poisson distribution with a mean of 7.
a.
What is the probability that on one particular day the officer gave out
no ticket?
b.
What is the probability that she gives out fewer than 4 tickets in one
day?
4.39
A Geiger counter counts the particles emitted by radioactive material. If
the number of particles emitted per second by a particular radioactive ma
terial has a Poisson distribution with a mean of 10 particles, determine the
following:
a.
The probability of at most 3 particles in one second.
b.
The probability of more than 1 particle in one second.
4.40
The number of cars that arrive at a drivein window of a certain bank over
a 20minute period is a Poisson random variable with a mean of four cars.
What is the probability that more than three cars will arrive during any 20
minute period?
4.41
The number of phone calls that arrive at a secretary’s desk has a Poisson
distribution with a mean of 4 per hour.
a.
What is the probability that no phone calls arrive in a given hour?
b.
What is the probability that more than 2 calls arrive within a given hour?
4.42
The number of typing mistakes that Ann makes on a given page has a Pois
son distribution with a mean of 3 mistakes.
a.
What is the probability that she makes exactly 7 mistakes on a given
page?
b.
What is the probability that she makes fewer than 4 mistakes on a given
page?
c.
What is the probability that Ann makes no mistake on a given page?
Section 4.8: Exponential Distribution
4.43
The PDF of a certain random variable
T
is given by
f
T
(
t
)
=
ke

4
t
t
≥
0
a.
What is the value of
k
?
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162
Chapter 4
Special Probability Distributions
b.
What is the expected value of
T
?
c.
Find
P
[
T
<
1
]
.
4.44
The lifetime
X
of a system in weeks is given by the following PDF:
f
X
(
x
)
=
braceleftbigg
0
.
25
e

0
.
25
x
x
≥
0
0
otherwise
a.
What is the expected value of
X
?
b.
What is the CDF of
X
?
c.
What is the variance of
X
?
d.
What is the probability that the system will not fail within two weeks?
e.
Given that the system has not failed by the end of the fourth week, what
is the probability that it will fail between the fourth and sixth weeks?
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 Fall '07
 Carlton
 Normal Distribution, Poisson Distribution, Probability, Probability theory, Exponential distribution

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