(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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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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