Textbook Problem

A bookstore at the Hartsfield-Jackson Airport in Atlanta sells reading materials (paperback 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.

		0	Reading Material 1	2
	0	0	60	18
Snacks	1	240	90	30
	2	120	30	12

1. a. 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?
2. b. Show the marginal probability distribution for the number of snack items purchased. Compute the expected value and variance.
3. c. What is the expected value and variance for the number of reading materials purchased by a customer?
4. d. Show the probability distribution for t = total number of items in a customer purchase. Compute its expected value and variance.

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?