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Lisa entered a fast food chain to eat, and the chain can serve the food within X minutes after she enters. Suppose further that she eats her food within Y minutes after it is served, independent of the serving time. Let Z = X + Y be the total amount of time that Lisa stays inside the fast food chain. The PDFs of the random variables X and Y are shown below: 0.1 i. ii. fx(x) 10 15 20 I fy (y) 0.1 E fy(y) = 0.1e-0.1y 50 Y What is the probability that Lisa stays within the fast food chain for at most 18 minutes, i.e. P(Z ≤ 18)? What is the expected value (in minutes) that Lisa stays within the fast food chain?

Lisa entered a fast food chain to eat, and the chain can serve the food within X minutes after she enters. Suppose further that she eats her food within Y minutes after it is served, independent of the serving time. Let Z = X + Y be the total amount of time that Lisa stays inside the fast food chain. The PDFs of the random variables X and Y are shown below: 0.1 i. ii. fx(x) 10 15 20 I fy (y) 0.1 E fy(y) = 0.1e-0.1y 50 Y What is the probability that Lisa stays within the fast food chain for at most 18 minutes, i.e. P(Z ≤ 18)? What is the expected value (in minutes) that Lisa stays within the fast food chain?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
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Lisa entered a fast food chain to eat, and the chain can serve the food within X minutes after she enters. Suppose further that she eats her food within Y minutes after it is served, independent of the serving time. Let Z = X + Y be the total amount of time that Lisa stays inside the fast food chain. The PDFs of the random variables X and Y are shown below: 0.1 i. ii. fx(x) 10 15 20 x fy (y) 0.1 E fy(y) = 0.1e-0.1y 50 Y What is the probability that Lisa stays within the fast food chain for at most 18 minutes, i.e. P(Z ≤ 18)? What is the expected value (in minutes) that Lisa stays within the fast food chain?
Transcribed Image Text:Lisa entered a fast food chain to eat, and the chain can serve the food within X minutes after she enters. Suppose further that she eats her food within Y minutes after it is served, independent of the serving time. Let Z = X + Y be the total amount of time that Lisa stays inside the fast food chain. The PDFs of the random variables X and Y are shown below: 0.1 i. ii. fx(x) 10 15 20 x fy (y) 0.1 E fy(y) = 0.1e-0.1y 50 Y What is the probability that Lisa stays within the fast food chain for at most 18 minutes, i.e. P(Z ≤ 18)? What is the expected value (in minutes) that Lisa stays within the fast food chain?
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