(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)
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)

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 =
+
+

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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