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 pX(x), what is P(X ≤ 1)?
e. Are X and Y independent rv's? Explain.