Assume that McDonalds can serve a customer's order in X minutes after the customer enters the fast food chain. The PDF of the random variable X is shown as: 0.1 10 Moreover, assume that the customer can finish the food Y minutes after it is served, independent of the serving time. The PDF of the random variable Y is shown as: JY(y) i. ii. fx(x) 0.1 fy(y) = 0.1e-0.1y 50 15 20 Let Z = X + Y be the total amount of time that the customer stays inside the fast food chain. Y What is the probability that the customer stays within McDonalds for at most 18 minutes, i.e. P(Z < 18)? What is the expected value (in minutes) that the customer stays within the fast food chain?
Assume that McDonalds can serve a customer's order in X minutes after the customer enters the fast food chain. The PDF of the random variable X is shown as: 0.1 10 Moreover, assume that the customer can finish the food Y minutes after it is served, independent of the serving time. The PDF of the random variable Y is shown as: JY(y) i. ii. fx(x) 0.1 fy(y) = 0.1e-0.1y 50 15 20 Let Z = X + Y be the total amount of time that the customer stays inside the fast food chain. Y What is the probability that the customer stays within McDonalds for at most 18 minutes, i.e. P(Z < 18)? What is the expected value (in minutes) that the customer stays within the fast food chain?
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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Transcribed Image Text:Assume that McDonalds can serve a customer's order in X minutes after the customer enters the fast food chain.
The PDF of the random variable X is shown as:
0.1
10
Moreover, assume that the customer can finish the food Y minutes after it is served, independent of the serving
time.
The PDF of the random variable Y is shown as:
i.
ii.
|fx(x)
0.1
fy(y)
fy(y) = 0.1e-0.1y
50
Let Z = X + Y be the total amount of time that the customer stays inside the fast food chain.
15 20
What is the probability that the customer stays within McDonalds for at most 18 minutes, i.e. P(Z <
18)?
What is the expected value (in minutes) that the customer stays within the fast food chain?
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