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Refer to Exercise 19.a. Compute the conditional mass

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

Solution for problem 21SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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

Statistics for Engineers and Scientists | 4th Edition

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Problem 21SE

Refer to Exercise 19.

a. Compute the conditional mass function PY|X(y|0.06).

b. Compute the conditional mass function PX|Y(x|100).

c. Compute the conditional expectation E(Y | X = 0.06).

d. Compute the conditional expectation  E(X | Y = 100).

Step-by-Step Solution:

Answer:

Step 1 of 5:  

                   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

 

Step 2 of 5:

a). To compute the conditional mass function

       Therefore,

                       

                                                 

                       = 0.138  

                       

                                                                   

                                                 = 0.276

                         

               

                                                 

                                                  = 0.586

                   

Step 3 of 5:

b). To compute the conditional mass function

          Therefore,

                       

                                                 

                                                  = 0.357

                           

                     

                                                     

                                                      = 0.071

                             

                    

                                                     

                                                       = 0.286

                               

                   

                                                                       

                                                      = 0.286

                                 = 0.286.

          

Step 4 of 5

Chapter 2, Problem 21SE is Solved
Step 5 of 5

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

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Refer to Exercise 19.a. Compute the conditional mass

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