A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the num- ber of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x, y) x 2 y 0 1 .10 .04 .08 .20 .06 .14 0800 88 2 .02 888 .06 .30

b. Compute P(X 1 and Y 1) from the joint probability table, and verify that it equals the product P(X 1). P(Y 1).

c. What is P(X + Y = 0) (the probability of no violations)?

d. Compute P(X + Y 1). 3.

A certain market has both an express checkout line and a superexpress checkout line. Let X, denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X, and X, is as given in the accompanying table.

a. What is P(X = 1 and Y = 1)?

b. Compute P(X 1 and Y 1).

c. Give a word description of the event {X+0 and Y 0}, and compute the probability of this event.

d. Compute the marginal pmf of X and of Y. Using px(x), what is P(X 1)?

e. Are X and Y independent rv's? Explain.