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) X y 1 2 0 0.10 0.03 0.02 0 1 0.06 0.20 0.07 2 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 At least one hose is in use at both islands. O One hose is in use on both islands. Compute the probability of this event. P(X = 0 and Y= 0) =
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) X y 1 2 0 0.10 0.03 0.02 0 1 0.06 0.20 0.07 2 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 At least one hose is in use at both islands. O One hose is in use on both islands. Compute the probability of this event. P(X = 0 and Y= 0) =
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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Transcribed Image Text:(d) Compute the marginal pmf of X.
X
Px(x)
0
Compute the marginal pmf of Y.
y
Py(Y)
0
Using Px(x), what is P(X ≤ 1)?
P(X ≤ 1) =
1
1
(e) Are X and Y independent rv's? Explain.
2
2
O X and Y are not independent because P(x,y) = Px(x) · Py(Y).
O X and Y are not independent because P(x,y) = Px(x) · Py(y).
O X and Y are independent because P(x,y) # Px(x)
Py(Y).
O X and Y are independent because P(x,y) = Px(x) Py(Y).
Transcribed Image Text: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
1
0
0.10 0.03 0.02
0.06
y
1 2
2 0.05
0.20 0.07
0.20
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 At least one hose is in use at both islands.
O One hose is in use on both islands.
Compute the probability of this event.
P(X = 0 and Y = 0) =
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