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Refer to Exercise 9.a. Find the conditional probability

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

Solution for problem 11E Chapter 2.6

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 11E

Refer to Exercise 9.

a. Find the conditional probability mass function pY|X(y|4).

b. Find the conditional probability mass function pX|Y(x|3).

c. Find the conditional expectation E(Y | X = 4).

d. Find the conditional expectation E(X | Y = 3).

Step-by-Step Solution:

Step 1 of 4:

 Bolt manufactured for a certain for a certain purpose classified as acceptable,downgraded or scrap. In a  lot of 500 bolts, if X denote the number of downgraded bolts, Y dente the number of scraps. The joint probability mass function of X and Y is given . here we can find the marginal probability function by adding the rows and columns.

Y

X

0

1

2

3

4

0

0.06

0.03

0.01

0

0

0.1

1

0.06

0.08

0.04

0.02

0

0.2

2

0.04

0.05

0.12

0.06

0.03

0.3

3

0

0.03

0.07

0.09

0.06

0.25

4

0

0

0.02

0.06

0.07

0.15

0.16

0.19

0.26

0.23

0.16

.

We have to find

The conditional probability mass function PY/X(y/4). The conditional probability mass function PX/Y(x/3). The conditional expectation E (Y/X=4). The conditional expectation E (X/Y=3).

Step 2 of 4:

 

 

The conditional probability mass function PY/X(y/4) have to find for different values of y. By using the table,

(i)   PY/X(0/4) =

                       =  

                       =   0

(ii)  PY/X(1/4)  =  

                       =  

                       =    0

(iii)  PY/X(2/4) =  

                       =    

                       =    

(iv)  PY/X(3/4)  = 

                        =    

                        =    

(v) PY/X(4/4)    =  

                       =    

                       =    

Step 3 of 3

Chapter 2.6, Problem 11E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 11E from chapter: 2.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: conditional, Find, expectation, Probability, mass. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “Refer to Exercise 9.a. Find the conditional probability mass function pY|X(y|4).________________b. Find the conditional probability mass function pX|Y(x|3).________________c. Find the conditional expectation E(Y | X = 4).________________d. Find the conditional expectation E(X | Y = 3).” is broken down into a number of easy to follow steps, and 36 words. Since the solution to 11E from 2.6 chapter was answered, more than 305 students have viewed the full step-by-step answer.

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