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 beshown that the total waiting time Y has the pdf below.1-y250 sy < 5f(y) =15 sy< 10525y < 0 or y > 10(a) Sketch a graph of the pdf of Y.f(y)f(y)f(y)0.20k0.20|0.20k0.150.150.150.100.100.100.050.050.05y10268102461048f(y)0.20|0.150.100.05y1068(b) Verify thatf(y) dy = 1.10f(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?

Answered: (e) What is the probability that total…

(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)

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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Question

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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 =
+
+

(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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