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(d) What is the probability that total waiting time is at most 9 min? 72 (e) What is the probability that total waiting time is between 1 and 9 min? () What is the probability that total waiting time is either less than 3 min or more than 7 min?

(d) What is the probability that total waiting time is at most 9 min? 72 (e) What is the probability that total waiting time is between 1 and 9 min? () What is the probability that total waiting time is either less than 3 min or more than 7 min?

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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In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 1 25 0 sy < 5 f(y) = 2 5 < ys 10 25 y < 0 or y > 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20 0.20 0.20아 0.20 0.15 0.15| 0.15 0.15 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 y 10 4 8 y 10 y 10 2 4 6. 8 10 4 6 8 4 6 8 (b) Verify that f(y) dy = 1. 1 2 10 f(y) dy = 25 + 2 50 5 + .5 (c) What is the probability that total waiting time is at most 1 min? .02 (d) What is the probability that total waiting time is at most 9 min? .72 (e) What is the probability that total waiting time is between 1 and 9 min? (f) What is the probability that total waiting time is either less than 3 min or more than 7 min?
Transcribed Image Text:In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 1 25 0 sy < 5 f(y) = 2 5 < ys 10 25 y < 0 or y > 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20 0.20 0.20아 0.20 0.15 0.15| 0.15 0.15 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 y 10 4 8 y 10 y 10 2 4 6. 8 10 4 6 8 4 6 8 (b) Verify that f(y) dy = 1. 1 2 10 f(y) dy = 25 + 2 50 5 + .5 (c) What is the probability that total waiting time is at most 1 min? .02 (d) What is the probability that total waiting time is at most 9 min? .72 (e) What is the probability that total waiting time is between 1 and 9 min? (f) What is the probability that total waiting time is either less than 3 min or more than 7 min?
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