Refer to Exercise 1 and answer the following questions: a. Given that X = 1, determine...

Refer to Exercise 1 and answer the following questions:

a. Given that X = 1, determine the conditional pmf of

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?

Reference Exercise 1

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 number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.

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 p_X(x), what is P(X ≤ 1)?

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