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) 1 0.10 0.03 0.02 (a) What is P(X-1 and Y-11 1) ? 0.05 0.14 0.33 P(X-1 and Y-1)-0.20 (b) Compute P(X ≤ 1 and Y≤ 1). P(X ≤ 1 and Y ≤1) - 0 (c) Give a word description of the event (X0 and Y/0). O One hose is in use on one island. O One hose is in use both islands. O At most one hose is in use at both islands. O At least one hose is in use at both islands. Compute the probability of this event. P(X0 and Y/0)- (d) Compute the marginal pmf of X. 0 Py(x) Compute the marginal pmf of y 1 1 Using P(x), what is P(X ≤ 1)? P(X≤1)-[ 2
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) 1 0.10 0.03 0.02 (a) What is P(X-1 and Y-11 1) ? 0.05 0.14 0.33 P(X-1 and Y-1)-0.20 (b) Compute P(X ≤ 1 and Y≤ 1). P(X ≤ 1 and Y ≤1) - 0 (c) Give a word description of the event (X0 and Y/0). O One hose is in use on one island. O One hose is in use both islands. O At most one hose is in use at both islands. O At least one hose is in use at both islands. Compute the probability of this event. P(X0 and Y/0)- (d) Compute the marginal pmf of X. 0 Py(x) Compute the marginal pmf of y 1 1 Using P(x), what is P(X ≤ 1)? P(X≤1)-[ 2
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: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)
(a) What is P(X= 1 and Y= 1) :
0 1
0 0.10 0.03 0.02
0.06 0.20 0.07
0.05 0.14 0.33
P(X= 1 and Y= 1) = 0.20
(b) Compute P(X ≤ 1 and Y < 1)
P(X ≤ 1 and Y≤ 1) =
(c) Give a word description of the event { X0 and Y0}.
O One hose is in use on one island.
O One hose is in use on both islands.
O At most one hose is in use at both islands.
O At least one hose is in use at both islands.
Compute the probability of this event.
P(X = 0 and Y # 0) =
Py(y)
(d) Compute the marginal pmf of X.
0
Px(x)
Compute the marginal pmf of Y.
0
2
1
Using P(x), what is P(X ≤ 1)?
P(X ≤1)=[
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