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Let Y1 denote the weight (in tons) of a bulk item stocked

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

Solution for problem 38E 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 38E

Problem 38E

Let Y1 denote the weight (in tons) of a bulk item stocked by a supplier at the beginning of a week and suppose that Y1 has a uniform distribution over the interval 0 ≤ y1 ≤ 1. Let Y2 denote the amount (by weight) of this item sold by the supplier during the week and suppose that Y2 has a uniform distribution over the interval 0 ≤ y2 ≤ y1, where y1 is a specific value of Y1.

a Find the joint density function for Y1 and Y2.

b If the supplier stocks a half-ton of the item, what is the probability that she sells more than a quarter-ton?

c If it is known that the supplier sold a quarter-ton of the item, what is the probability that she had stocked more than a half-ton?

Step-by-Step Solution:

Solution

Step 1 of 3

a) Let Y1 is the weight of the bulk

And Y1 has a uniform distribution with the interval means (0,1)

Then

Let Y2 is the amount of the item sold

And Y2 has a uniform distribution with the intervalmeans(0,y1)

Then

We know

                 =

                                 =

                                 =

 Hence


                             

Step 2 of 3

Chapter 5, Problem 38E 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 Y1 denote the weight (in tons) of a bulk item stocked