Question

In: Economics

A market researcher wants to determine whether a new model of a personal computer that had...

A market researcher wants to determine whether a new model of a personal computer that had been advertised on a​ late-night talk show had achieved more​ brand-name recognition among people who watched the show regularly than among people who did not. After conducting a​ survey, it was found that 16​%of all people both watched the show regularly and could correctly identify the product.​ Also,20​% of all people regularly watched the show and 45​%of all people could correctly identify the product. Define a pair of random variables as shown below. Complete parts​ (a) through​ (c).

X

=

1

if regularly watch the show

X

=

0

otherwise

Y

=

1

if product correctly identified

Y

=

0

otherwise

a. Find the joint probability function of X and Y.

X

0

1

Y

0

1

​(Do not​ round.)

b. Find the conditional probability function of​ Y, givenX=1.

​P(0​|1= ​(Round to three decimal places as​ needed.)

​P(1​|1​)= ​(Round to three decimal places as​ needed.)

c. Find and interpret the covariance between X and Y.

​Cov(X,Y)= (Do not​ round.)

Interpret the covariance.

A.The covariance indicates that there is a positive association between watchers of a​ late-night talk show and​ brand-name recognition.

B.The covariance indicates that there is a negative association between watchers of a​ late-night talk show and​ brand-name recognition.

C.The covariance indicates that there is no association between watchers of a​ late-night talk show and​ brand-name recognition.

Solutions

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