In: Economics
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.