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Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
Figure 14: Probability Density Function f(x) = exp(x), 0 x 15
For the second probability density function:
15
0
c
2
xdx =
225
2
c
2
= 1 = c
2
=
2
225
= 8.8889 ×10
3
,
f(x) = 8.8889 × 10
3
x, 0 x 15.
The probability density function is shown in Figure 15.
Figure 15: Probability Density Function f(x) = 8.888 9 ×10
3
x, 0 x 15
36
The mean, variance, standard deviation, and coefficient of variation are given by
µ =
15
0
8.8889 ×10
3
x
2
dx = 10.0
V ar(X) =
15
0
x
2
8.8889 ×10
3
x dx 10
2
= 12.5
σ =
V ar(X) =
12.5 = 3.5355
δ =
σ
µ
= 3.5355/10 = 0.35355.
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Publisher Resources

ISBN: 9781439849897