The Chamber of Commerce in a Canadian city has conducted an evaluation of the 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 and 3 highest). The data are summarised here:

a) From the data, 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.

b) Compute the expected value and variance for quality rating, x.

c) Compute the expected value and variance for meal price, y.

d) Overall ratings of a restaurant are often based on a composite of ratings on different dimensions. Assume that price x and quality y are the only dimensions measured, so that the composite rating would be the sum x + y. Find the probability distribution of x + y and compute Var(x + y).

	Meal Price
Quality	1	2	3	Total
1	42	39	3	84
2	33	63	54	150
3	3	15	48	66
Total	78	117	105	300

e) Compute the covariance of x and y. Comment on the relationship between quality and price.

f) Compute the correlation coefficient between quality rating and meal price. What is the strength of the relationship?

g) Do you suppose that it is likely to find a low-cost restaurant in this city that is of high quality? Why or why not?