10. [-/9.61 Points] DETAILS DEVORESTAT9 5.1.001.MI. MY NOTES ASK YOUR TEACHER 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) 0 0 0.10 0.05 0.01 1 0.06 0.20 0.08 0.06 0.14 0.30 (a) What is P(X = 1 and Y = 1)? P(X = 1 and Y = 1) = (b) Compute P(X s 1 and Y S 1). P(X S 1 and Y S 1) = (c) Give a word description of the event {X # 0 and Y # 0}. O At most one hose is in use at both islands. O One hose is in use on both islands. O At least 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) = (d) Compute the marginal pmf of X. 2 Px ( x ) Compute the marginal pmf of Y. 2 Pyly Using p (x), what is P(X S 1)? P(X s 1) = (e) Are X and Y independent rv's? Explain. O X and Y are independent because P(x,y) = Px(x) . Py(y). O X and Y are not independent because P(x,y) # Px(x) . Py(y). O X and Y are not independent because P(x,y) = Px(x) . Py(y). O X and Y are independent because P(x,y) # Px(x) . Py(y)