Chapter 5.1, Problem 18E

Refer to Exercise 1 and answer the following questions:

1. a. Given that X = 1, determine the conditional pmf of Y—i.e., p_{Y | X}(0 | 1), p_{Y | X}(1 | 1), and p_{Y | X}(2 | 1).
2. 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?
3. c. Use the result of part (b) to calculate the conditional probability P(Y ≤ 1 | X = 2).
4. 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?