3. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. Let Y denote the waiting time (in minutes) for the school bus. Assume the total waiting time Y has the pdf Osy<5 5 25 5 sys 10 y < 0 or y > 10 a. Sketch a graph of the pdf of Y. b. Verify that , fy)dy =1. 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?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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3. In commuting to work, a professor must first get on a bus near her house
and then transfer to a second bus. Let Y denote the waiting time (in minutes) for the
school bus. Assume the total waiting time Y has the pdf
0sy< 5
25
1
5 sys 10
25
y < 0 or y > 10
a. Sketch a graph of the pdf of Y.
b. Verify that f)dy =1.
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?
Transcribed Image Text:3. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. Let Y denote the waiting time (in minutes) for the school bus. Assume the total waiting time Y has the pdf 0sy< 5 25 1 5 sys 10 25 y < 0 or y > 10 a. Sketch a graph of the pdf of Y. b. Verify that f)dy =1. 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?
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