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.

	y
p(x, y)		0	1	2
x	0	0.10	0.05	0.02
1	0.06	0.20	0.07
2	0.05	0.14	0.31

(a) What is P(X = 1 and Y = 1)?

(b) Compute P(X 1 and Y 1).

(c) Compute the probability of this event.

(d) Compute the marginal pmf of X.

x	0	1	2
pX(x)

Compute the marginal pmf of Y.

y	0	1	2
pY(y)

(e) Using p_X(x), what is P(X 1)?