Can you please help? I'll give a like!

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 3 0.01 Y 1 0.07 0.20 0.07 0.05 0.14 0.33 (a) What is P(X = 1 and Y = 1)? P(X = 1 and Y = 1) = (b) Compute P(X = 1 and Y = 1). P(X = 1 and Y = 1) = (c) Give a word description of the event {X = 0 and Y = 0}. O One hose is in use on one island. 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. Compute the probability of this event. P(X # 0 and Y = 0) =[ (d) Compute the marginal pmf of X. 0 1 2 PX(x) Compute the marginal pmf of Y. 0 2 py(v) Using p (x), what is P(X = 1)? P(X = 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) = p (x) . py(v). O X and Y are independent because P(x,y) # px(x) . py(v). O X and Y are not independent because P(x,y) = px(x) . py(y)