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Chapter 5: Q 5.40 (page 214)
If is uniformly distributed over, find the density function of.
Therefore, the PDF of
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(a) A fire station is to be located along a road of length . If fires occur at points uniformly chosen on localid="1646880402145" , where should the station be located so as to minimize the expected distance from the fire? That is,
choose a so as to minimize localid="1646880570154" when X is uniformly distributed over .
(b) Now suppose that the road is of infinite length鈥� stretching from point outward to . If the distance of a fire from point is exponentially distributed with rate , where should the fire station now be located? That is, we want to minimize , where X is now exponential with rate .
Let X have probability density f X. Find the probability density function of the random variable Y defined by Y = a X + b.
For some constant c, the random variable X has the probability density function:
Find
Let be a random variable with probability density function
(a) What is the value of?
(b) What is the cumulative distribution function of?
The following table uses data concerning the percentages of male and female full-time workers whose
annual salaries fall into different ranges:
Suppose that random samples of 200 male and 200 female full-time workers are chosen. Approximate the probability
that
(a) at least of the women earn or more;
(b) at most percent of the men earn or more;
(c) at least three-fourths of the men and at least half the women earn or more.
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