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Solved: Differentiate the moment-generating function in

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 148E Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 148E

Problem 148E

Differentiate the moment-generating function in Exercise 3.147 to find E(Y ) and E(Y 2). Then find V (Y ).

Reference

If Y has a geometric distribution with probability of success p, show that the moment-generating function for Y is

Step-by-Step Solution:
Step 1 of 3

Solution 148E

Step1 of 3:

We have a random variable ‘Y’ and it follows geometric distribution with parameter ‘p’.

Then the probability mass function of geometric distribution is given by:

Where,

x = random variable

p = probability of success(Parameter)

n = sample size

Also we have moment generating function of Y is .

We need to find mean and variance of geometric distribution by using moment generating function.


Step2 of 3:

Consider,

       

The mean of geometric distribution is given by:

       

                     

                                     

                                 

                       

Hence,

Now,

           

                 

Therefore, The mean of geometric distribution is


Step3 of 3:

Consider,

From step 2, We know that

Now,

         

                                           

                                             

                                               

                       

Hence,  

Now,

                 

                   

                     

                           

                     

                 

Therefore, .

The variance of geometric distribution is given by:

       

             

Therefore, The variance of geometric distribution is .


Step 2 of 3

Chapter 3, Problem 148E is Solved
Step 3 of 3

Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

The full step-by-step solution to problem: 148E from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Since the solution to 148E from 3 chapter was answered, more than 1746 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Find, moment, generating, function, geometric. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The answer to “Differentiate the moment-generating function in Exercise 3.147 to find E(Y ) and E(Y 2). Then find V (Y ).ReferenceIf Y has a geometric distribution with probability of success p, show that the moment-generating function for Y is” is broken down into a number of easy to follow steps, and 37 words. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811.

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