(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
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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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