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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 43
probability density function is
p(x) =
Γ((k + 1)/2)
Γ(k/2)
1
1
(1 + x
2
/k)
(k+1)/2
, x R,
where Γ is the gamma function defined by (2.103). The mean and variance
are given by
E(X) = 0 if k > 1 (otherwise undefined),
and
Var(X) = k/(k 2) if k > 2 (otherwise undefined).
Figure 2.10 compares the pr obability density function of a Student’s t dis-
tribution with various deg rees of freedom to the probability density function
of a standard normal distribution. From this figure we see that the proba-
bility density function of a Student’s t distribution is symmetric like that of
the no rmal distribution, with “heavier tails,” ...
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Publisher Resources

ISBN: 9781482206432