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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
3.6. Random variable X is continuous and its values are governed by f
X
(x) or F
X
(x). If random variable
Y = 2X, derive an expression for f
Y
(y) and F
Y
(y).
Solution: Consider a simple case where f
X
(x) = 1 for 0 x < 1. The corresponding cumulative distribution
is F
X
(x) = x for 0 x < 1 and F
X
(x) = 1 for x 1. We wish to use another random variable, Y, that is
related to our original random variable, X, by Y = 2X.
The probability does not change even when the random variables change. That is,
F
y
(y) = F
X
(2x) .
For example, Pr (x < 1/2) = 1/2 = F
X
(x = 1/2) = F
Y
(y = 2x = 1) . We apply the same principle for the
incremental probability,
Pr (x X x +
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Publisher Resources

ISBN: 9781439849897