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) a 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. f(y) = 2 5 0.15 1 25 0 1 25 0 ≤y<5 5 ≤ y ≤ 10 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) 0.20k f(y) 0.20 0.15
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) a 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. f(y) = 2 5 0.15 1 25 0 1 25 0 ≤y<5 5 ≤ y ≤ 10 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) 0.20k f(y) 0.20 0.15
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Please solve a, b, c, d, 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
5, then it can be shown that the total waiting time Y has the pdf below.
has a uniform distribution with A = 0 and B
=
f(y)
f(y)
0.20
0.15
0.10
(a) Sketch a graph of the pdf of Y.
0.05
f(y)
f(y)
0.20
0.15
VV
0.10
0.05
y
10
0.20
0.15
0.10
0.05
2
(b) Verify that
["anor=[
f(y) dy =
1
25
2
-
2
0
+ [ f(y)
1
25
4
4
0 ≤ y ≤ 5
5 ≤ y ≤ 10
y <0 or y> 10
f(y) dy = 1.
5
0
6
6
+
8
co
8
10
10
5
f(y)
0.20
0.15
0.10
0.05
2
2
4
4
6
8
6 8
y
10
10
y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afdb6c4-3a61-4c47-91da-dfd2e9ec1a67%2Fcbe48f5b-3381-4b28-ac80-12fa153d5bc3%2Fjzswo76_processed.png&w=3840&q=75)
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
5, then it can be shown that the total waiting time Y has the pdf below.
has a uniform distribution with A = 0 and B
=
f(y)
f(y)
0.20
0.15
0.10
(a) Sketch a graph of the pdf of Y.
0.05
f(y)
f(y)
0.20
0.15
VV
0.10
0.05
y
10
0.20
0.15
0.10
0.05
2
(b) Verify that
["anor=[
f(y) dy =
1
25
2
-
2
0
+ [ f(y)
1
25
4
4
0 ≤ y ≤ 5
5 ≤ y ≤ 10
y <0 or y> 10
f(y) dy = 1.
5
0
6
6
+
8
co
8
10
10
5
f(y)
0.20
0.15
0.10
0.05
2
2
4
4
6
8
6 8
y
10
10
y
![(b) Verify that
[ FLY
-∞
2
[ F(X)
f(y) dy =
f(y) dy = 1.
= = 1/2 + (
0
6 8
+
10
y..
105
(c) What is the probability that total waiting time is at most 3 min?
2.0
(d) What is the probability that total waiting time is at most 7 min?
(e) What is the probability that total waiting time is between 3 and 7 min?
2
4
(f) What is the probability that total waiting time is either less than 2 min or more than 8 min?
6 8
10
y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afdb6c4-3a61-4c47-91da-dfd2e9ec1a67%2Fcbe48f5b-3381-4b28-ac80-12fa153d5bc3%2F16vc8up_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Verify that
[ FLY
-∞
2
[ F(X)
f(y) dy =
f(y) dy = 1.
= = 1/2 + (
0
6 8
+
10
y..
105
(c) What is the probability that total waiting time is at most 3 min?
2.0
(d) What is the probability that total waiting time is at most 7 min?
(e) What is the probability that total waiting time is between 3 and 7 min?
2
4
(f) What is the probability that total waiting time is either less than 2 min or more than 8 min?
6 8
10
y
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