The joint pmf of X and Y is f (x, y) = 1/6, 0 ?x + y ? 2,

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

Problem 6E 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 6E

PROBLEM 6E

The joint pmf of X and Y is f (x, y) = 1/6, 0 ≤x + y ≤ 2, where x and y are nonnegative integers.

(a) Sketch the support of X and Y.

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

(c) Compute Cov(X,Y).

(d) Determine ρ, the correlation coefficient.

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

Step-by-Step Solution:

Answer

Step 1 of  8

a) Construct a table for a given pmf        0

     

y x

0

1

2

0

1/6

1/6

1/6

3/6

1

1/6

1/6

0

2/6

2

1/6

0

0

1/6

3/6

2/6

1/6

1

Step 2 of  8

b)  Marginal pmf of x is

x

0

1

2

Total

3/6

2/6

1/6

1

 

     Marginal pmf of y is

y

0

1

2

Total

3/6

2/6

1/6

1

Step 3 of  8

c) Now find the mean and variance by using the tables

E(X) = 

         =0(3/6)+1(2/6)+2(1/6)

        =4/6

E(Y)=

       =0(3/6)+1(2/6)+2(1/6)

        =4/6

E(XY)=

          =1(1)(⅙)

          =1/6

cov(X,Y)=E(XY)-E(X)E(Y)

               =1/6-4/6(4/6)

               = -10/36

Step 4 of  8

d)E(X2)=

         =0(3/6)+1(2/6)+4(1/6)

         =1

=V(x)

      =E(X2) -[ E(X)]2 

      =1- (4/6)2

      =20/36

Step 5 of 7

Chapter 4.2, Problem 6E is Solved
Step 6 of 7

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

Since the solution to 6E from 4.2 chapter was answered, more than 257 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 6E from chapter: 4.2 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. The answer to “The joint pmf of X and Y is f (x, y) = 1/6, 0 ?x + y ? 2, where x and y are nonnegative integers.(a) Sketch the support of X and Y.(b) Record the marginal pmfs fX(x) and fY(y) in the “margins.”(c) Compute Cov(X,Y).(d) Determine ?, the correlation coefficient.(e) Find the best-fitting line and draw it on your figure.” is broken down into a number of easy to follow steps, and 60 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9th. This full solution covers the following key subjects: Best, coefficient, correlation, cov, determine. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271.

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