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P(X #0 and Y# 0) = d) Compute the marginal pmf of X. 0 x Px (x) Compute the marginal pmf of Y. 0 y Using P(x), what is P(X ≤ 1)? P(X ≤ 1) = 1 1 (e) Are X and Y independent rv's? Explain. 2 2 O X and Y are not independent because P(x,y) = P(x). P,(y). O X and Y are not independent because P(x,y) #P(x) - p,(y). O X and Y are independent because P(x,y) #Px(x). p,(y). O X and Y are independent because P(x,y) = P(x). P,(y).

P(X #0 and Y# 0) = d) Compute the marginal pmf of X. 0 x Px (x) Compute the marginal pmf of Y. 0 y Using P(x), what is P(X ≤ 1)? P(X ≤ 1) = 1 1 (e) Are X and Y independent rv's? Explain. 2 2 O X and Y are not independent because P(x,y) = P(x). P,(y). O X and Y are not independent because P(x,y) #P(x) - p,(y). O X and Y are independent because P(x,y) #Px(x). p,(y). O X and Y are independent because P(x,y) = P(x). P,(y).

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 (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) = [ y 0 1 2 0.10 0.03 0.01 0.07 0.20 0.08 0.05 0.14 0.32 (c) Give a word description of the event {X = 0 and Y# 0}. O At least one hose is in use at both islands. One hose is in use on both islands. 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) = [ y Py(y) (d) Compute the marginal pmf of X. 0 Px (x) Compute the marginal pmf of Y. 0 Using P(x), what is P(X ≤ 1)? P(X ≤ 1) = 1 1 (e) Are X and Y independent rv's? Explain. 2 2 O X and Y are not independent because P(x,y) = Px(x) - P₁(y). O X and Y are not independent because P(x,y) = Px(x) - P₂(y). O X and Y are independent because P(x,y) # Px(x) - P₂(y). O X and Y are independent because P(x,y) = Px(x) - P₂(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) 0 1 2 (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) = [ y 0 1 2 0.10 0.03 0.01 0.07 0.20 0.08 0.05 0.14 0.32 (c) Give a word description of the event {X = 0 and Y# 0}. O At least one hose is in use at both islands. One hose is in use on both islands. 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) = [ y Py(y) (d) Compute the marginal pmf of X. 0 Px (x) Compute the marginal pmf of Y. 0 Using P(x), what is P(X ≤ 1)? P(X ≤ 1) = 1 1 (e) Are X and Y independent rv's? Explain. 2 2 O X and Y are not independent because P(x,y) = Px(x) - P₁(y). O X and Y are not independent because P(x,y) = Px(x) - P₂(y). O X and Y are independent because P(x,y) # Px(x) - P₂(y). O X and Y are independent because P(x,y) = Px(x) - P₂(y).
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