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Chapter 5: Q:5.3 (page 217)
For some constant c, the random variable X has the probability density function:
Find
a. The value of
b.
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Let be a lognormal random variable (see Example 7e for its definition) and let be a constant. Answer true or false to the following, and then give an explanation for your answer.
(a) is lognormal;
(b) is lognormal.
A fire station is to be located along a road of length. If fires occur at points uniformly chosen on, where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to
minimize
whenis uniformly distributed over
Now suppose that the road is of infinite length鈥� stretching from point outward to. If the distance of fire from the point is exponentially distributed with rate, where should the fire station now be located? That is, we want to minimize, where is now exponential with rate.5.6. Computeif has a density function given by
;
;
.
If is a normal random variable with parameters and , compute
(a)role="math" localid="1646719347104"
(b)role="math" localid="1646719357568"
(c)role="math" localid="1646719367217"
(d)
(e)
At a certain bank, the amount of time that a customer spends being served by a teller is an exponential random variable with mean minutes. If there is a customer in service when you enter the bank, what is the probability that he or she will still be with the teller after an additional minutes?
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