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?