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Using the joint pmf from Exercise 4.2-3, find the value of

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

Solution for problem 7E Chapter 4.3

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 7E

PROBLEM 7E

Using the joint pmf from Exercise 4.2-3, find the value of E(Y | x) for x = 1, 2, 3, 4. Do the points [x, E(Y | x)] lie on the best-fitting line?

Step-by-Step Solution:

Step 1 of 12:

Lex the joint probability mass function of X and Y be

f(x,y)=; (x,y)=(0,1),(1,0),(2,1)

The number of variables corresponding to x is not equal to the number of variables corresponding to y. So the support is not rectangular. Hence X and Y are dependent.

Mean of X,=1 and mean of Y, =.

Therefore

  Cov(X,Y)=E(XY)- 

                 =(0)(1)+(1)(0)+(2)(1)-1()

                 =0+0+-

                 =0

Thus correlation coefficient  becomes equal to 0, which implies X and Y are independent. But we have that X and Y are dependent.

Step 2 of 12:

Consider an experiment of rolling a  fair four sided die.Let x denotes the outcome on the first roll of the die and Y denotes the sum of the outcomes of the two rolls.

Therefore X takes the values X={1,2,3,4} and Y takes the values Y={2,3,4,5,6,7,8}.

Also  x+1 and y

Since the  die is a fair die, the joint probability mass function of  X and Y becomes

f(x,y)=; x=1,2,3,4 and y=2,3,4,5,6,7,8

Step 3 of  12:

X denotes the outcomes of rolling  a four sided fair die.

Therefore the  marginal probability mass function of X becomes

f(x) =; x=1,2,3,4

Step 4 of 12:

We have to find the value of E(Y|x) at x=1,2,3,4.

E(Y|x) is given by            

E(Y|x)=yh(y|x)

where  h(y|x) is the conditional probability mass function of Y given X=x.

Now we have to find h(y|x)

h(y|x)=

          =

         = 

Step 5 of 8

Chapter 4.3, Problem 7E is Solved
Step 6 of 8

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

The answer to “Using the joint pmf from Exercise 4.2-3, find the value of E(Y | x) for x = 1, 2, 3, 4. Do the points [x, E(Y | x)] lie on the best-fitting line?” is broken down into a number of easy to follow steps, and 33 words. The full step-by-step solution to problem: 7E from chapter: 4.3 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. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since the solution to 7E from 4.3 chapter was answered, more than 320 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Best, exercise, Find, fitting, Joint. This expansive textbook survival guide covers 59 chapters, and 1476 solutions.

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