×
Log in to StudySoup
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2 - Problem 20se
Join StudySoup for FREE
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2 - Problem 20se

Already have an account? Login here
×
Reset your password

Refer to Exercise 19.a. Find ?X.________________b. Find

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 20SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 1 289 Reviews
20
5
Problem 20SE

Problem 20SE

Refer to Exercise 19.

a. Find μX.

b. Find μY.

c. Find σX.

d. Find σY.

e. Find Cov(X, Y).

f. Find ρX,Y.

Step-by-Step Solution:
Step 1 of 3

Answer:

Step1 of 7:

          From exercise 19.

The joint probability mass function of tensile strength (y) and additive concentration (x).

                   

       

 

                   Tensile strength (y)

Concentration of additive (x)

 100

150

200

0.02

0.05

0.06

0.11

0.22

0.04

0.01

0.08

0.10

0.19

0.06

0.04

0.08

0.17

0.29

0.08

0.04

0.14

0.12

0.3

0.14

0.36

0.5

 


Step2 of 7: 

a). We need to find .

     That is,

                 

                

                        = 0.02(0.22) + 0.04(0.19) + 0.06(0.29) + 0.08(0.3)

                        = 0.0534.

         Therefore, = 0.0534.


Step3 of 7:

b). To find

     That is,

                     

                 

                          = 100(0.14) + 150(0.36) + 200(0.5)

                          = 168.

            Therefore, = 168.


 Step4 of 7:

 c). To find

      That is,

                   

                                       

                          =(0.22) +

                          = 0.00050444

   

       

        = 0.02246.

Therefore, = 0.02246.


  Step5 of 7:

 d). To find

        That is,

                   

                         

                     

                     = 1276.

              

     

                   = 35.7211

 Therefore, = 35.7211


 Step6 of 7:

 e). To find Cov(X,Y).

     Then,

               

         Now,

                  =

                          

+

 (0.08)(100)P(0.08 and 100) + (0.08)(150)P(0.08 and 150) + (0.08)(200)P(0.08 and 200).

 

  

+

 (0.08)(100)(0.04) + (0.08)(150)(0.14) + (0.08)(200)(0.12).

      = 8.96.

  Therefore,

                 

                                     = 8.96 - (0.0534)(168)

                                     = 8.96 - 8.9712

                                     = - 0.0112.

          Therefore,


  Step7 of 7:

  f). To find

           

         

                      =

                     

                      = -0.01396

         Therefore,

                         


 

 

       

         

Step 2 of 3

Chapter 2, Problem 20SE is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Refer to Exercise 19.a. Find ?X.________________b. Find