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Refer to Exercise 5.149.a Find E(Y2|Y1 = y1).b Use Theorem

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

Solution for problem 150SE Chapter 5

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 150SE

Problem 150SE

Refer to Exercise 5.149.

a Find E(Y2|Y1 = y1).

b Use Theorem 5.14 to find E(Y2).

c Find E(Y2) directly from the marginal density of Y2.

Reference

Let Y1 and Y2 have a joint density function given by

a Find the marginal density functions of Y1 and Y2.

b Find P(Y1 ≤ 3/4|Y2 ≤ 1/2).

c Find the conditional density function of Y1 given Y2 = y2.

d Find P(Y1 ≤ 3/4|Y2 = 1/2).

Step-by-Step Solution:

Solution:

Step 1 of 3:

Let Y1 and Y2 have a joint density function given by,

           

We have to find,

  1. E(Y2/Y1=y1).
  2. E(Y2).
  3. E(Y2) by using the marginal density of Y2.

Step 2 of 3

Chapter 5, Problem 150SE 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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Refer to Exercise 5.149.a Find E(Y2|Y1 = y1).b Use Theorem