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

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Chapter1: Functions
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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
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
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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