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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
Probability and Statistics Overview 23
related to the first and second moments through the relationship
Var(X) = E
(X E(X))
2
= E
X
2
2XE(X) + (E(X))
2
= E(X
2
) (E(X))
2
.
(2.46)
One of the useful concepts in understanding the variation of a random
variable X is the coefficient of variation (CV), which is defined as the r atio of
the standard deviation to the mean (that is, CV =
p
Var(X)/E(X)). It is the
inverse of the so-calle d signal-to-noise ratio. A random variable with CV < 1
is considered to have low variatio n, while one with CV > 1 is considered to
have high variation.
Note that the moments of a function of a random variable, Y = η(X), can
be defined
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Publisher Resources

ISBN: 9781482206432