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) у 0 1 0 0.10 0.03 0.02 1 0.06 0.20 0.08 2 0.06 0.14 0.31 (a) What is P(X= 1 and Y= 1)? P(X= 1 and Y = 1) = 0.20 (b) Compute P(X ≤ 1 and Y s 1). P(X ≤ 1 and Y≤ 1) = 0.39 (c) Give a word description of the event (X = 0 and Y 0). O One hose is in use on both islands. At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on one island. Compute the probability of this event. P(X 0 and Y 0) 0.73 (d) Compute the marginal pmf of X. 0 Px(x) 0.15 Compute the marginal pmf of Y. 0.34 0 2 Py(y) 0.22 Using px(x), what is P(X ≤ 1)? P(X ≤ 1) = 0.5 X ✓ 0.37 1 0.51 0.41 2 2

Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter6: Circles
Section6.CT: Test
Problem 11CT: aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _
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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
(a) What is P(X = 1 and Y = 1)?
P(X= 1 and Y = 1) = 0.20
(b) Compute P(X ≤ 1 and
y
1
0
0.10 0.03 0.02
1 0.06 0.20 0.08
2 0.06 0.14 0.31
X
P(X ≤ 1 and Y ≤ 1) = 0.39
0
(c) Give a word description of the event {X # 0 and Y # 0}.
O One hose is in use on both islands.
O At least one hose is in use at both islands.
O At most one hose is in use at both islands.
O One hose is in use on one island.
PX(X) 0.15
y
Compute the probability of this event.
0.73
P(X 0 and Y = 0)
(d) Compute the marginal pmf of X.
Y ≤ 1).
Py(y) 0.22
0
Compute the marginal pmf of Y.
0
0.34
2
0.37
Using Px(x), what is P(X ≤ 1)?
P(X ≤ 1) = 0.5
X
1
1
0.51
0.41
2
2
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) X (a) What is P(X = 1 and Y = 1)? P(X= 1 and Y = 1) = 0.20 (b) Compute P(X ≤ 1 and y 1 0 0.10 0.03 0.02 1 0.06 0.20 0.08 2 0.06 0.14 0.31 X P(X ≤ 1 and Y ≤ 1) = 0.39 0 (c) Give a word description of the event {X # 0 and Y # 0}. O One hose is in use on both islands. O At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on one island. PX(X) 0.15 y Compute the probability of this event. 0.73 P(X 0 and Y = 0) (d) Compute the marginal pmf of X. Y ≤ 1). Py(y) 0.22 0 Compute the marginal pmf of Y. 0 0.34 2 0.37 Using Px(x), what is P(X ≤ 1)? P(X ≤ 1) = 0.5 X 1 1 0.51 0.41 2 2
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