Refer to Exercise 1 and answer the following questions:

a. Given that X
1, determine the conditional pmf of Y—i.e., pY⏐X (0⏐1), pY⏐X (1⏐1), and pY⏐X (2⏐1).

b. Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island?

c. Use the result of part

(b) to calculate the conditional probability P(Y  1⏐X
2).

d. Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island?