4.80 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 15% of all people both watched the show regularly and could correctly identify the product. Also, 16% of all people regularly watched the show and 45% of all people could correctly identify the product. Define a pair of random variables as follows:

X = 1 if regularly watch the show X = 0 otherwise Y = 1 if product correctly identified Y = 0 otherwise

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

b. Find the conditional probability distribution of Y, given X = 1.

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