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In a smoking survey among boys between the ages of 12 and

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

Solution for problem 8E Chapter 4.1

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 8E

PROBLEM 8E

In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date nonsmokers, 1% prefer to date smokers, and 21% don’t care. Suppose seven such boys are selected randomly. Let X equal the number who prefer to date nonsmokers and Y equal the number who prefer to date smokers.

(a) Determine the joint pmf of X and Y. Be sure to include the support of the pmf.

(b) Find the marginal pmf of X. Again include the support.

Step-by-Step Solution:

Answer:

Step 1 of 2 :

Given,

In a smoking survey among boys between the ages of 12 and 17.

Here 78% prefer to date non smokers.

78% = 0.78

1% prefer to date smokers.

1% = 0.01 and

21% don’t care.

21% = 0.21

We know that seven boys are selected randomly.

Let X equal the number who prefer to date non smokers and

Let Y equal the number who prefer to date smokers .

PMF(x,y) = Prob {X prefer non smokers, Y prefer smokers}

Our goal is to find

a). Determine the joint pmf of X and Y.Be sure to include the support of the pmf.

b).Find the marginal pmf of X.Again include the support.

a).

Now we have to determine the joint pmf of X and Y.

We know that prefer to date non smokers is 0.78, prefer to date smokers is 0.01,don’t care is 0.21 and n=7.

Then the joint pmf X and Y is

 

Where

 

Hence the the joint pmf of X and Y is above.

Step 2 of 2

Chapter 4.1, Problem 8E is Solved
Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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