Customers at a fast-food restaurant buy both sandwiches and drinks. The following joint distribution summarizes the numbers of sandwiches ( ) and drinks ( ) purchased by customers. (a) Find the...

Customers at a fast-food restaurant buy both sandwiches and drinks. The following joint distribution summarizes the numbers of sandwiches () and drinks () purchased by customers.

(a) Find the expected value and variance of the number of sandwiches.

(b) Find the expected value and variance of the number of drinks.

(c) Find the correlation between
. (Hint: You might find the calculations easier if you use the alternative expression for the covariance shown in the Formulas section at the end of the chapter.)

(d) Interpret the size of the correlation for the manager of the restaurant.

(e) If the profit earned from selling a sandwich is $1.50 and from a drink is $1.00, what is the expected value and standard deviation of the profit made from each customer?

(f) Find the expected value of the ratio of drinks to sandwiches. Is it the same as