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. p(x, y) у 0 1 0 0.10 0.03 0.02 1 0.06 0.20 0.08 2 0.06 0.14 0.31 (a) What is P(X= 1 and Y= 1)? P(X= 1 and Y = 1) = 0.20 (b) Compute P(X ≤ 1 and Y s 1). P(X ≤ 1 and Y≤ 1) = 0.39 (c) Give a word description of the event (X = 0 and Y 0). O One hose is in use on both islands. At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on one island. Compute the probability of this event. P(X 0 and Y 0) 0.73 (d) Compute the marginal pmf of X. 0 Px(x) 0.15 Compute the marginal pmf of Y. 0.34 0 2 Py(y) 0.22 Using px(x), what is P(X ≤ 1)? P(X ≤ 1) = 0.5 X ✓ 0.37 1 0.51 0.41 2 2