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In a process of sintering (heating) two types of copper

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

Solution for problem 14E Chapter 6

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 14E

Problem 14E

In a process of sintering (heating) two types of copper powder (see Exercise 5.152), the density function for Y1, the volume proportion of solid copper in a sample, was given by

Reference

In the production of a certain type of copper, two types of copper powder (types A and B) are mixed together and sintered (heated) for a certain length of time. For a fixed volume of sintered copper, the producer measures the proportion Y1 of the volume due to solid copper (some pores will have to be filled with air) and the proportion Y2 of the solid mass due to type A crystals. Assume that appropriate probability densities for Y1 and Y2 are

The proportion of the sample volume due to type A crystals is then Y1Y2. Assuming that Y1 and Y2 are independent, find P(Y1Y2 ≤ .5).

Step-by-Step Solution:
Step 1 of 3

Solution 14E

Step1 of 2:

Let us consider the random variables denotes two types of copper powder, the density function for is given by:

The density function for , the proportion of type A crystal among the solid copper, was given as:

 

We need to find the probability density function of U.


Step2 of 2:

Let us assume that  are independent so,

 

                                                                                     

Where, , .

Then

Now,

               

                 

                                     

                                             

                                             

                                             

                                                               

                                                               

                           

Now,

 

                                     

                           

Therefore, the probability density function of U is given by:


Step 2 of 3

Chapter 6, Problem 14E is Solved
Step 3 of 3

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

Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. The answer to “In a process of sintering (heating) two types of copper powder (see Exercise 5.152), the density function for Y1, the volume proportion of solid copper in a sample, was given by ReferenceIn the production of a certain type of copper, two types of copper powder (types A and B) are mixed together and sintered (heated) for a certain length of time. For a fixed volume of sintered copper, the producer measures the proportion Y1 of the volume due to solid copper (some pores will have to be filled with air) and the proportion Y2 of the solid mass due to type A crystals. Assume that appropriate probability densities for Y1 and Y2 are The proportion of the sample volume due to type A crystals is then Y1Y2. Assuming that Y1 and Y2 are independent, find P(Y1Y2 ? .5).” is broken down into a number of easy to follow steps, and 138 words. This full solution covers the following key subjects: copper, proportion, Volume, solid, type. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Since the solution to 14E from 6 chapter was answered, more than 1795 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 14E from chapter: 6 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM.

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In a process of sintering (heating) two types of copper