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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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A telephone call arrived at a switchboard at random within

Chapter 4, Problem 49E

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QUESTION:

Problem 49E

A telephone call arrived at a switchboard at random within a one-minute interval. The switch board was fully busy for 15 seconds into this one-minute period. What is the probability that the call arrived when the switchboard was not fully busy?

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QUESTION:

Problem 49E

A telephone call arrived at a switchboard at random within a one-minute interval. The switch board was fully busy for 15 seconds into this one-minute period. What is the probability that the call arrived when the switchboard was not fully busy?

ANSWER:

Solution 49E

Step1 of 2:

Let us consider a random variable Y it presents the number of calls arrived at a switchboard within a one-minute interval. The switch-board was fully busy for 15 seconds into this one-minute period.

We need to find the probability that the call arrived when the switchboard was not fully busy.

Step2 of 2:

Here X follows uniform distribution with parameter a and b.

Where,

a = 0 and b = 1.

Then,

The density function of Y is given by:

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