MATH Q 13

13. [-/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 1 2 0 0.10 0.03 0.01 X 1 0.06 0.20 0.07 2 0.05 0.14 0.34 (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}. At most one hose is in use at both islands. O At least one hose is in use at both islands. O One hose is in use on one island. O One hose is in use on both islands. Compute the probability of this event. P(X # 0 and Y # 0) =(d) Compute the marginal pmf of X. X 0 1 2 PX ( x ) Compute the marginal pmf of Y. 0 2 py(y ) Using py(x), what is P(X