A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with twohoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number ofhoses 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)X0(a) What is P(X = 1 and Y = 1)?P(X= 1 and Y = 1) =Xy1(b) Compute P(X ≤ 1 and Y ≤ 1).P(X ≤ 1 and Y ≤ 1) =yPy(y)0 0.10 0.05 0.021 0.06 0.20 0.08(c) Give a word description of the event {X = 0 and Y # 0}.O At most one hose is in use at both islands.2 0.05 0.14 0.30O One hose is in use on both islands.O One hose is in use on one island.O At least one hose is in use at both islands.0Compute the probability of this event.P(X 0 and Y # 0) =(d) Compute the marginal pmf of X.02Px(x)Compute the marginal pmf of Y.11Using p(x), what is P(X ≤ 1)?P(X ≤ 1) =(e) Are X and Y independent rv's? Explain.22O X and Y are independent because P(x,y) = Px(x) · Py(Y).O X and Y are not independent because P(x,y) # Px(x) · Py(Y).X and Y are independent because P(x,y) = P(x) · Py(y).O X and Y are not independent because P(x,y) = Px(x) • Py(y).

A service station has both self-service and full-service islands. On each island, there is a single…

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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(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}.