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DingAngBato enters a restaurant and queues in line to order his favorite food. Suppose that the restaurant can serve his favorite food within X minutes after DingAngBato enters the restaurant. Suppose further that DingAngBato eats his food within Y minutes after it is served, independent of the serving time. Let W = X + Y be the total amount of time that DingAngBato stays inside the restaurant The PDFs of the random variables X and Y are shown below

DingAngBato enters a restaurant and queues in line to order his favorite food. Suppose that the restaurant can serve his favorite food within X minutes after DingAngBato enters the restaurant. Suppose further that DingAngBato eats his food within Y minutes after it is served, independent of the serving time. Let W = X + Y be the total amount of time that DingAngBato stays inside the restaurant The PDFs of the random variables X and Y are shown below

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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DingAng Bato enters a restaurant and queues in line to order his favorite food. Suppose that the restaurant can serve his favorite food within X minutes after DingAngBato enters the restaurant. Suppose further that DingAngBato eats his food within Y minutes after it is served, independent of the serving time. Let W = X + Y be the total amount of time that DingAngBato stays inside the restaurant. The PDFs of the random variables X and Y are shown below. 0.1 fx(x) ● 10 15 20 x 0.1 fx (y) fy(y) = 0.1e-0.1y 50 Y What is the probability that DingAngBato stays within the restaurant for at most 18 minutes, i.e. P(W≤18)? (Hint: Answer is not 0.9459 nor 0.9462) What is the expected value (in minutes) that DingAngBato stays within the restaurant? (Hint: Answer is not 5.4043 nor 14.999)
Transcribed Image Text:DingAng Bato enters a restaurant and queues in line to order his favorite food. Suppose that the restaurant can serve his favorite food within X minutes after DingAngBato enters the restaurant. Suppose further that DingAngBato eats his food within Y minutes after it is served, independent of the serving time. Let W = X + Y be the total amount of time that DingAngBato stays inside the restaurant. The PDFs of the random variables X and Y are shown below. 0.1 fx(x) ● 10 15 20 x 0.1 fx (y) fy(y) = 0.1e-0.1y 50 Y What is the probability that DingAngBato stays within the restaurant for at most 18 minutes, i.e. P(W≤18)? (Hint: Answer is not 0.9459 nor 0.9462) What is the expected value (in minutes) that DingAngBato stays within the restaurant? (Hint: Answer is not 5.4043 nor 14.999)
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