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If the moment-generating function of a random variable W

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 9E Chapter 3.2

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 9E

If the moment-generating function of a random variable W is

M ( t ) = (1 − 7t )−20,

find the pdf, mean, and variance of W.

Step-by-Step Solution:

Answer :

Step 1 of 2 :

Given,

The moment-generating function of a random variable W is  M(t) = (1 - 7t.

The claim is to find the pdf, mean and variance of W

We know that the moment generating function of X is

M(t) =

         =

Where,  = 7 and  = 20

The probability density function of gamma distribution is

f(x) = , x0

f(x) = , x0

f(x) = , x0


Step 2 of 2

Chapter 3.2, Problem 9E is Solved
Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

This full solution covers the following key subjects: Find, function, generating, mean, moment. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. The answer to “If the moment-generating function of a random variable W isM ( t ) = (1 ? 7t )?20,find the pdf, mean, and variance of W.” is broken down into a number of easy to follow steps, and 25 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since the solution to 9E from 3.2 chapter was answered, more than 351 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 9E from chapter: 3.2 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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If the moment-generating function of a random variable W