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(c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 8 min?

(c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 8 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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I think I've figured out a) so I only need the rest

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 -y 25 0 sy < 5 f(y) = 1 5 sy< 10 5 25 y < 0 or y > 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) 0.20k 0.20| 0.20k 0.15 0.15 0.15 0.10 0.10 0.10 0.05 0.05 0.05 y 10 2 6 8 10 2 4 6 10 4 8 f(y) 0.20| 0.15 0.10 0.05 y 10 6 8 (b) Verify that f(y) dy = 1. 10 f(y) dy = + +
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 -y 25 0 sy < 5 f(y) = 1 5 sy< 10 5 25 y < 0 or y > 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) 0.20k 0.20| 0.20k 0.15 0.15 0.15 0.10 0.10 0.10 0.05 0.05 0.05 y 10 2 6 8 10 2 4 6 10 4 8 f(y) 0.20| 0.15 0.10 0.05 y 10 6 8 (b) Verify that f(y) dy = 1. 10 f(y) dy = + +
(c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 8 min? (e) What is the probability that total waiting time is between 3 and 8 min? (f) What is the probability that total waiting time is either less than 2 min or more than 9 min?
Transcribed Image Text:(c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 8 min? (e) What is the probability that total waiting time is between 3 and 8 min? (f) What is the probability that total waiting time is either less than 2 min or more than 9 min?
Expert Solution
Step 1

Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART from b to d

HERE GIVEN probability density function of total waiting time

 

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