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The number N of residential homes that a fire company can
Chapter 3, Problem 21E(choose chapter or problem)
The number N of residential homes that a fire company can serve depends on the distance r (in
city blocks) that a fire engine can cover in a specified (fixed) period of time. If we assume that
N is proportional to the area of a circle R blocks from the firehouse, then \(N=C \pi R^{2}\), where C is a constant, \(\pi=3.1416\)..., and R, a random variable, is the number of blocks that a fire engine can move in the specified time interval. For a particular fire company, \(C=8\), the probability distribution for R is as shown in the accompanying table, and \(p(r)=0\) for \(r \leq 20\) and \(r \geq 27\).
r |
21 |
22 |
23 |
24 |
25 |
26 |
\(p(r)\) |
.05 |
.20 |
.30 |
.25 |
.15 |
.05 |
Find the expected value of N, the number of homes that the fire department can serve.
Equation Transcription:
Text Transcription:
N=CpiR^2
pi=3.1416
C=8
p(r)=0
r</=20
r>/=27
p(r)
Questions & Answers
QUESTION:
The number N of residential homes that a fire company can serve depends on the distance r (in
city blocks) that a fire engine can cover in a specified (fixed) period of time. If we assume that
N is proportional to the area of a circle R blocks from the firehouse, then \(N=C \pi R^{2}\), where C is a constant, \(\pi=3.1416\)..., and R, a random variable, is the number of blocks that a fire engine can move in the specified time interval. For a particular fire company, \(C=8\), the probability distribution for R is as shown in the accompanying table, and \(p(r)=0\) for \(r \leq 20\) and \(r \geq 27\).
r |
21 |
22 |
23 |
24 |
25 |
26 |
\(p(r)\) |
.05 |
.20 |
.30 |
.25 |
.15 |
.05 |
Find the expected value of N, the number of homes that the fire department can serve.
Equation Transcription:
Text Transcription:
N=CpiR^2
pi=3.1416
C=8
p(r)=0
r</=20
r>/=27
p(r)
ANSWER:
Solution
Step 1 of 2
We have to find the expected no. of homes the fire department can serve
Give that N is the no.of homes the fire department can serve
And
Given that C=8
=3.1416
The probability distribution of r is given by
r |
21 |
22 |
23 |
24 |
25 |
26 |
Total |
P(r) |
0.05 |
0.2 |
0.3 |
0.25 |
0.15 |
0.05 |
1 |
r |
1.05 |
4.4 |
6.9 |
6 |
3.75 |
1.3 |
23.4 |
Now E(r)=
=23.4