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A car dealer sells X cars each day and always tries to

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 9E Chapter 4.2

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 9E

PROBLEM 9E

A car dealer sells X cars each day and always tries to sell an extended warranty on each of these cars. (In our opinion, most of these warranties are not good deals.) Let Y be the number of extended warranties sold; then Y ≤ X. The joint pmf of X and Y is given by

(a) Find the value of c.

(b) Sketch the support of X and Y.

(c) Record the marginal pmfs fX(x) and fY(y) in the “margins.”

(d) Are X and Y independent?

(e) Compute μX and

(f) Compute μY and

(g) Compute Cov(X,Y).

(h) Determine ρ, the correlation coefficient.

(i) Find the best-fitting line and draw it on your figure.

Step-by-Step Solution:

Answer

Step 1 of 14</p>

Here we are finding the value of c for that we need to arrange the values in the table

The given joint pmf is given by

                   x=0,1,2,3     y=0,1,2   with  y

By using the given pmf form a table

Y

0

1

2

3

0

12c

18c

18c

12c

60c

1

0

24c

24cc

16c

64c

2

0

0

18c

12c

30c

12c

42c

60c

40c

154c

Step 2 of 14</p>

a) Since the total probability is one

   

           154c=1

                 c=1/154

Step 3 of 14</p>

b) Substitute the c value in the above table

 

Y

0

1

2

3

0

12/154

18/154

18/154

12/154

60/154

1

0

24/154

24/154

16/154

64/154

2

0

0

18/154

12/154

30/154

12/154

42/154

60/154

40/154

154/154=1

Step 4 of 5

Chapter 4.2, Problem 9E is Solved
Step 5 of 5

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. This full solution covers the following key subjects: compute, Find, these, Warranties, extended. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Since the solution to 9E from 4.2 chapter was answered, more than 460 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 9E from chapter: 4.2 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. The answer to “A car dealer sells X cars each day and always tries to sell an extended warranty on each of these cars. (In our opinion, most of these warranties are not good deals.) Let Y be the number of extended warranties sold; then Y ? X. The joint pmf of X and Y is given by (a) Find the value of c.(b) Sketch the support of X and Y.(c) Record the marginal pmfs fX(x) and fY(y) in the “margins.”(d) Are X and Y independent?(e) Compute ?X and (f) Compute ?Y and (g) Compute Cov(X,Y).(h) Determine ?, the correlation coefficient.(i) Find the best-fitting line and draw it on your figure.” is broken down into a number of easy to follow steps, and 108 words.

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