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=1if 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.