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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}.

(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}.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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 0 (a) What is P(X = 1 and Y = 1)? P(X= 1 and Y = 1) = X y 1 (b) Compute P(X ≤ 1 and Y ≤ 1). P(X ≤ 1 and Y ≤ 1) = y Py(y) 0 0.10 0.05 0.02 1 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 0.30 O 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. 0 Compute the probability of this event. P(X 0 and Y # 0) = (d) Compute the marginal pmf of X. 0 2 Px(x) Compute the marginal pmf of Y. 1 1 Using p(x), what is P(X ≤ 1)? P(X ≤ 1) = (e) Are X and Y independent rv's? Explain. 2 2 O 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).
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 0 (a) What is P(X = 1 and Y = 1)? P(X= 1 and Y = 1) = X y 1 (b) Compute P(X ≤ 1 and Y ≤ 1). P(X ≤ 1 and Y ≤ 1) = y Py(y) 0 0.10 0.05 0.02 1 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 0.30 O 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. 0 Compute the probability of this event. P(X 0 and Y # 0) = (d) Compute the marginal pmf of X. 0 2 Px(x) Compute the marginal pmf of Y. 1 1 Using p(x), what is P(X ≤ 1)? P(X ≤ 1) = (e) Are X and Y independent rv's? Explain. 2 2 O 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).
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