I need letters d and e 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)P(X= 1 and Y0(a) What is P(X= 1 and Y: 1) ?y00.10 0.03 0.021 0.06 0.20 0.082 0.05 0.14 0.321(b) Compute P(X≤ 1 and Y≤ 1).Py(y)P(X ≤ 1 and Y < 1) 0.391) = 0.200(c) Give a word description of the event { X0 and Y #0}.O One hose is in use on both islands.O One hose is in use on one island.O At most one hose is in use at both islands.ⒸAt least one hose is in use at both islands.Compute the probability of this event.P(X #0 and Y 0) = 0.74(d) Compute the marginal pmf of X.0Px(x)Compute the marginal pmf of Y.211Using p(x), what is P(X < 1)?P(X ≤1)=[(e) Are X and Y independent rv's? Explain.OX and Y are independent because P(x, y) #Px (1) - Py (Y).OX and Y are not independent because P(x, y) ‡ Px(z) · Py(Y).OX and Y are independent because P(x, y) = Px(z) - py(y).OX and Y are not independent because P(x, y) = Px(z) - Pr (y).

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(d) Compute the marginal pmf of X. Compute the marginal pmf of Y P, Using p(x), what is P(X ≤ 1)? P(X≤1)= 2 (e) Are X and Y independent rv's? Explain. OX and Yare independent because P(z,y)/Px(z)-Py(). OX and Yare not independent because P(z)/Px(z)-Py(). OX and Yare independent because P(x,y)=Px(z) Py(). OX and Yare not independent because P(z,y)=Px(2)-Py().