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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi
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The time between requests to a web server is exponentially

Chapter 4, Problem 2E

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QUESTION:

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

a. What is the value of the parameter \(\lambda\)?

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 more than

one additional second will elapse before the next request?

Equation transcription:

Text transcription:

lambda

Questions & Answers

QUESTION:

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

a. What is the value of the parameter \(\lambda\)?

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 more than

one additional second will elapse before the next request?

Equation transcription:

Text transcription:

lambda

ANSWER:

Solution

 

Step 1 of 7

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

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