Reference no: EM132422248

Problem: Sheila, a market researcher is interested in assessing whether a new model of a vacuum cleaner that has been advertised on a radio talk show had achieved more brand name recognition among people who listened to the show regularly than among people who did not. Upon conducting a survey, she finds that 15% of all people both listened to the show regularly and could correctly identify the product. Also, 16% of all people regularly listened to the show and 45% of all people could correctly identify the product. Define a pair of random variables as follows: P = 1, if regularly listened to the show; P = 0, otherwise. S = 1, if product identified correctly; S = 0, otherwise.

Required:

Question 1: Find the joint probability distribution of P and S.

Question 2: Find the conditional probability function of S, given P = 1.

Question 3: Find the correlation coefficient between P and S.