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Suppose that Y has a beta distribution with parameters ?

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

Solution for problem 200SE Chapter 4

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 200SE

Problem 200SE

Suppose that Y has a beta distribution with parameters α and β.

a If a is any positive or negative value such that α + a > 0, show that

b Why did your answer in part (a) require that α + a > 0?

c Show that, with a = 1, the result in part (a) gives E(Y ) = α/(α + β).

d Use the result in part (a) to give an expression for E( Y ). What do you need to assume about α?

e Use the result in part (a) to give an expression for E(1/Y ), E(1/ Y ), and E(1/Y 2). What do you need to assume about α in each case?

Step-by-Step Solution:

Answer:

Step 1 of 5:

(a)

Suppose that  has a beta distribution with parameters

If  is any positive or negative value such that  show that

A random variable  is said to have a beta probability distribution with parameters

if and only if the density function of  is

…………(1)

Where,

…………..(2)

We know the expected value of any random variable,

Hence,

[ is defined in the range of ]

[using equation (2)]

……(3)

We know from equation (2),

Hence compare the integral of equation (2) and (3), our parameter  will become

………..(4)

Hence proved.


Step 2 of 5

Chapter 4, Problem 200SE is Solved
Step 3 of 5

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

This full solution covers the following key subjects: part, result, use, assume, show. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. Since the solution to 200SE from 4 chapter was answered, more than 257 students have viewed the full step-by-step answer. The answer to “Suppose that Y has a beta distribution with parameters ? and ?.a If a is any positive or negative value such that ? + a > 0, show that b Why did your answer in part (a) require that ? + a > 0?c Show that, with a = 1, the result in part (a) gives E(Y ) = ?/(? + ?).d Use the result in part (a) to give an expression for E( ? Y ). What do you need to assume about ??e Use the result in part (a) to give an expression for E(1/Y ), E(1/ ? Y ), and E(1/Y 2). What do you need to assume about ? in each case?” is broken down into a number of easy to follow steps, and 116 words. The full step-by-step solution to problem: 200SE from chapter: 4 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. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811.

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