The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 re

Question

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 (1 lowest to 3 highest) on typical meal price and quality (1 lowest to 3 highest). 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, 36 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 Quality 2 36 60 24 120 Total 81 144 75 300 42 54 48 105 30 Total 75 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 ymeal price Round your answers to two decimal places. Meal Price y Quality Total Total

Explanation / Answer

here dividing each cell by 300 to get joint probability distribution:

b) marginal probability of x:

c)

marginal density of Y:

d )

1st method

(we can find by Covar(X,Y)=(1.6691-0.5196-0.59)/2=0.2797)  

2nd method

E(XY) = 4.44

hence Covar(X,Y) =E(XY)-E(X)E(Y) =0.2820

e) correlation =Cov(X,Y)/(Var(X)*Var(Y)) =0.5093

y x 1 2 3 Total 1 0.1400 0.1200 0.0100 0.2700 2 0.1000 0.2000 0.1800 0.4800 3 0.0100 0.0800 0.1600 0.2500 Total 0.2500 0.4000 0.3500 1.0000

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