1. A bookstore at the Hartsfield-Jackson Airport in Atlanta sells reading materials (paper-back books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.). A point-of-sale terminal collects a variety of information about customer purchases. Shown below is a table showing the number of snack items and the number of items of reading material purchased by the most recent 600 customers. Snacks (1) 0 1 0 0 240 20 Reading Material (y) 1 60 90 30 2 18 30 12 I (a) [10 points] Using the data in the table construct an empirical discrete bivariate probability distribution for r = number of snack items and y = number of reading materials in a randomly selected customer purchase. What is the probability of a customer purchase consisting of one item of reading materials and two snack items? What is the probability of a customer purchasing one snack item only? Why is the probability f(x = 0, y = 0) = 0? (b) [10 points] Show the marginal probability distribution for the number of snack items pur- chased. Compute the expected value and variance. (c) [10 points] What is the expected value and variance for the number of reading materials purchased by a customer? (d) [10 points] Show the probability distribution for t = total number of items in a customer purchase. Compute its expected value and variance. (e) [10 points] Compute the covariance and correlation coefficient between x and y. What is the relationship, if any, between the number of reading materials and number of snacks purchased on a customer visit?

1. A bookstore at the Hartsfield-Jackson Airport in Atlanta sells reading materials (paper-back books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.). A point-of-sale terminal collects a variety of information about customer purchases. Shown below is a table showing the number of snack items and the number of items of reading material purchased by the most recent 600 customers. (a) [10 points] Using the data in the table construct an empirical discrete bivariate probability distribution for x= number of snack items and y= number of reading materials in a randomly selected customer purchase. What is the probability of a customer purchase consisting of one item of reading materials and two snack items? What is the probability of a customer purchasing one snack item only? Why is the probability f(x=0,y=0)=0 ? (b) [10 points] Show the marginal probability distribution for the number of snack items purchased. Compute the expected value and variance. (c) [10 points] What is the expected value and variance for the number of reading materials purchased by a customer? (d) [10 points] Show the probability distribution for t= total number of items in a customer purchase. Compute its expected value and variance. (e) [10 points] Compute the covariance and correlation coefficient between x and y. What is the relationship, if any, between the number of reading materials and number of snacks purchased on a customer visit