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Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t. Find the

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

Solution for problem 155E 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 155E

Problem 155E

Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t. Find the following:

a E ( Y )

b V ( Y )

c The distribution of Y

Step-by-Step Solution:

Solution:

Step 1 of 3:

                        Let

  a). To find

        By the definition of moment generating function is

                                      

If Y = 1,  = 

If Y = 2,   = 

If Y = 3,   = 

           Then the expected value is

                                         

                                                   =

                                                   =  

                         Therefore,


Step 2 of 3

Chapter 3, Problem 155E is Solved
Step 3 of 3

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

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Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t. Find the