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P₂(x) Compute the marginal pmf of Y. P, (v) 0 1 Using P(x), what is P(X ≤ 1)? P(X ≤1)=[ 2 e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(z,y) #Px(z) - Py(V). OX and Y are independent because P(z,y) = Px(z) - Py (y). OX and Y are not independent because P(z,y) = Px(z) - Py(y). OX and Yare independent because Plz.11) +11~(7). Th.. (11).

P₂(x) Compute the marginal pmf of Y. P, (v) 0 1 Using P(x), what is P(X ≤ 1)? P(X ≤1)=[ 2 e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(z,y) #Px(z) - Py(V). OX and Y are independent because P(z,y) = Px(z) - Py (y). OX and Y are not independent because P(z,y) = Px(z) - Py(y). OX and Yare independent because Plz.11) +11~(7). Th.. (11).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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) 0 1 2 0 y 1 (a) What is P(X= 1 and Y= 0.10 0.05 0.01 0.06 0.20 0.07 0.05 0.14 0.32 = 1)? P(X= 1 and Y = 1) = [0.20 2 (b) Compute P(X≤ 1 and Y≤ 1). P(X ≤ 1 and Y≤1) 0.41 (c) Give a word description of the event { X= 0 and Y #0}. At least one hose is in use at both islands. At most one hose is in use at both islands. O One hose is in use on both islands. O One hose is in use on one island. Compute the probability of this event. P(X0 and Y 0) = 0.90
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 2 0 y 1 (a) What is P(X= 1 and Y= 0.10 0.05 0.01 0.06 0.20 0.07 0.05 0.14 0.32 = 1)? P(X= 1 and Y = 1) = [0.20 2 (b) Compute P(X≤ 1 and Y≤ 1). P(X ≤ 1 and Y≤1) 0.41 (c) Give a word description of the event { X= 0 and Y #0}. At least one hose is in use at both islands. At most one hose is in use at both islands. O One hose is in use on both islands. O One hose is in use on one island. Compute the probability of this event. P(X0 and Y 0) = 0.90
(d) Compute the marginal pmf of X. x 0 Px(x) Compute the marginal pmf of Y. y Py(V) 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(z) - Py(y). OX and Y are independent because P(x, y) = Px(z)-Py (y). OX and Y are not independent because P(x, y) = Px(z) - Py(y). OX and Y are independent because P(x, y) #Px (2) - Py (Y).
Transcribed Image Text:(d) Compute the marginal pmf of X. x 0 Px(x) Compute the marginal pmf of Y. y Py(V) 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(z) - Py(y). OX and Y are independent because P(x, y) = Px(z)-Py (y). OX and Y are not independent because P(x, y) = Px(z) - Py(y). OX and Y are independent because P(x, y) #Px (2) - Py (Y).
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