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The time between requests to a web server is exponentially

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 2E Chapter 4.7

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 2E

The time between requests to a web server is exponentially distributed with mean 0.5 seconds.

a. What is the value of the parameter λ?

b. What is the median time between requests?

c. What is the standard deviation?

d. What is the 80th percentile?

e. Find the probability that more than one second elapses between requests.

f. If there have been no requests for the past two seconds, what is the probability that there more than one additional second will elapse before the next request?

Step-by-Step Solution:

 

Step 1 of 7</p>

Here time is exponentially distributed with mean 0.5 seconds

Then =0.5

The Pmf of exponential distribution is

The CDF of exponential distribution is

Step 2 of 7</p>

a) Here We have to find the value of the parameter

Given  =0.5

      Then =2

Step 3 of 7</p>

b) We have to find the median

Let a be the median

Then P(Xa)=0.5

        =0.5

              =0.5

                         2a=0.6931

                              a=0.34655

Hence the median is 0.34655

Step 4 of 7</p>

c) Here we have to find the standard deviation 

The standard deviation of exponential distribution is

Then

                =

      =0.5

Hence the standard deviation is 0.5

Step 5 of 7

Chapter 4.7, Problem 2E is Solved
Step 6 of 7

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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