Please help me solve this problem!

3. (Exercise 1 on p. 242 of MMSA, Revised) A service station has a self-service and a full-service islands. On each island, there is a single regular unleaded pump with 2 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 is shown in the table below. y (full service) p(x, y) 0 1 2 0 0.10 0.04 0.02 (self 0.08 0.20 0.06 service) 2 0.06 0.14 0.30 (a) What is the probability that the 4 hoses are all in use? (b) What is the probability that only 1 of the 4 hoses are in use, P(X + Y = 1)? (c) Compute the marginal pmf px of X. (d) Compute the marginal pmf py of Y. (e) Find the probability that the 2 hoses in the self-service island are both in use. (f) Given that the 2 hoses in the self-service island are both in use (X = 2), find the conditional pmf PYIX=2(y|2) of Y. (g) Given that neither of the 2 hoses in the full-service island is in use (Y = 0), find the conditional pmf PXly=0(x|0) of X. (h) Are X and Y independent rv's? Explain