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(d) Compute the marginal pmf of X. 0 Px(x) Compute the marginal pmf of Y. y Py(y) 0 1 1 Using px(x), what is P(X < 1)? P(X ≤ 1) = [ 2 2 (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(x, y) = Px(x) · Py(y). OX and Y are independent because P(x, y) ‡ px(x) · py(y).

(d) Compute the marginal pmf of X. 0 Px(x) Compute the marginal pmf of Y. y Py(y) 0 1 1 Using px(x), what is P(X < 1)? P(X ≤ 1) = [ 2 2 (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(x, y) = Px(x) · Py(y). OX and Y are independent because P(x, y) ‡ px(x) · py(y).

A First Course in Probability (10th Edition)
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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(d) Compute the marginal pmf of X. 0 Px(x) Compute the marginal pmf of Y. y Py(y) 1 1 Using px(x), what is P(X < 1)? P(X ≤ 1) = [ 2 2 (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(x, y) = Px(x) · Py(y). OX and Y are independent because P(x, y) ‡ px(x) · py(y). OX and Y are independent because P(x, y) = Px(x) - Py(y). OX and Y are not independent because P(x, y) # px(x) · py(y).
Transcribed Image Text:(d) Compute the marginal pmf of X. 0 Px(x) Compute the marginal pmf of Y. y Py(y) 1 1 Using px(x), what is P(X < 1)? P(X ≤ 1) = [ 2 2 (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(x, y) = Px(x) · Py(y). OX and Y are independent because P(x, y) ‡ px(x) · py(y). OX and Y are independent because P(x, y) = Px(x) - Py(y). OX 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 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 0.05 0.01 1 0.06 0.20 0.07 2 0.05 0.14 0.32 (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) = | 2 (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 One hose is in use on both islands. O At least one hose is in use at both islands. Compute the probability of this event. P(X0 and Y # 0) =
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 0.05 0.01 1 0.06 0.20 0.07 2 0.05 0.14 0.32 (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) = | 2 (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 One hose is in use on both islands. O At least one hose is in use at both islands. Compute the probability of this event. P(X0 and Y # 0) =
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