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(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?

(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?

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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I only need e) and f) 

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?
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Note: Since you have asked for subparts (e) and (f) that is why only these two subparts have been answered. 

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