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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
3.12. Derive Equation 3.12.
Solution: This is the equation for the variance of X. Expanding the square under the integral and considering
each term individually, the result is obtained.
31
3.13. Continuous random variable X is governed by the probability density function
f(x) =
1, 0 x 1
0, otherwise.
Evaluate E{e
X
}.
Solution: The expected value of e
X
is given by
E{e
X
} =
e
x
f (x) dx
=
1
0
e
x
dx
= e
x
|
1
0
= e 1.
32
3.14. For the random variable X we are given
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Publisher Resources

ISBN: 9781439849897