The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a rating on a 3-point scale on typical meal price (1 least expensive to 3 most expensive) and quality (1 lowest quality to 3 greatest quality). A crosstabulation of the rating data is shown below. Forty-two of the restaurants received a rating of 1 on quality and 1 on meal price, 39 of the restaurants received a rating of 1 on quality and 2 on meal price, and so on. Forty-eight of the restaurants received the highest rating of 3 on both quality and meal price.
Meal Price (y)
Quality (x) 1 2 3 Total
1 42 39 3 84
2 33 54 63 150
3 6 12. 48 66
Total 81 105 114 300
(a) Develop a bivariate probability distribution for quality and meal price of a randomly selected restaurant in this Canadian city. Let x quality rating and y = meal price
Meal Price (y)
Quality (x) 1 2 3 Total
1 - - -
2 - - -
3 - - -
Total
(b) Compute the expected value and variance for quality rating, x.
(c) Compute the expected value and variance for meal price, y.