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Let X and Y have a trinomial distribution with n = 2, pX =

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

Solution for problem 5E 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 5E

PROBLEM 5E

Let X and Y have a trinomial distribution with n = 2, pX = 1/4, and pY = 1/2.

(a) Give E(Y | x).

(b) Compare your answer in part (a) with the equation of the line of best fit in Example 4.2-2. Are they the same? Why or why not?

References Example 4.2-2

Step-by-Step Solution:

Step 1 of 5 :

We have that X and Y have the trinomial distribution with n=2, p(X)=and p(Y)=.

The joint probability mass function of x and Y is given as

f(x,y)=

         =:0

Step 2 of 5:

(a)

We have to find the conditional expectation of Y given X.

That is we have to find E(Y|X=x)

The marginal probability mass function of X is given by

f(x)=f(x,y)

     =

    =

The property of trinomial distribution states that the marginal; distribution of the variables X and Y is Binomial.

Therefore X~b(2,)

Step 3 of 5:

The conditional probability mass function of Y given X=x is given by

                                                            h(y|x)=

                                                       =

                                                               =

                           =

Step 4 of 5

Chapter 4.3, Problem 5E is Solved
Step 5 of 5

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

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