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For continuous random variables X and Y with joint

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

Solution for problem 16E 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 16E

For continuous random variables X and Y with joint probability density function

 

a. Find P(X > 1 and Y > 1).

b. Find the marginal probability density functions fX(x) and fY(y).

c. Are X and Y independent? Explain.

Step-by-Step Solution:
Step 1 of 3

Solution 16E

Step1 of 3:

We have continuous random variables X and Y with joint probability density function

Here our goal is:

a).We need to find P(X > 1 and Y > 1).

b).We need to find the marginal probability density functions  

c).We need to check Are X and Y independent? Explain.

Step2 of 3:

a).

Consider,

 

                                                

Integrate above equation with respect to “y” we get

                                                

                                 

                                 =    

                                    = 0 - (-)

                           =

Where “e” is mathematical constant and its value is approximately 2.71828. Substitute “e” i above equation we get

                                      =

                                                                            =

                                                                            =

                                                                            = 0.0676

Therefore, = 0.0676.

Step3 of 3:

b).

Consider,

1).If Therefore, ) = 0.

2).If Then

                =

 ...

Step 2 of 3

Chapter 2.6, Problem 16E is Solved
Step 3 of 3

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

The full step-by-step solution to problem: 16E from chapter: 2.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 16E from 2.6 chapter was answered, more than 261 students have viewed the full step-by-step answer. The answer to “For continuous random variables X and Y with joint probability density function a. Find P(X > 1 and Y > 1).________________b. Find the marginal probability density functions fX(x) and fY(y).________________c. Are X and Y independent? Explain.” is broken down into a number of easy to follow steps, and 36 words. This full solution covers the following key subjects: Density, Probability, Find, independent, function. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

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