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Let Y be a discrete random variable with mean ? and

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

Solution for problem 33E 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 33E

Problem 33E

Let Y be a discrete random variable with mean μ and variance σ 2. If a and b are constants, use Theorems 3.3 through 3.6 to prove that

a E ( aY + b) = aE(Y ) + b = + b.

b V ( aY + b) = a2 V (Y ) = a2σ 2.

Reference

Step-by-Step Solution:

 Solution:

Step 1 of 3:

    Here we need to prove that

 a).

 b).

Step 2 of 3

Chapter 3, Problem 33E 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 Y be a discrete random variable with mean ? and