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Abstract

The PDF, CDF, and CF of a Gaussian RV \( {\rm X} \in N_n \left( {\bar {\rm X},\sigma ^2 } \right) \) are given in (1.1), (1.2), and (1.5) respectively with σx replaced by σ. For \( \bar {\rm X} = 0 \), the even moments of the components of X are given by
$$ E\left\{ {X_i^{2k} } \right\} = \overline {X_i^{2k} } = \frac{{\left( {2k} \right)!}} {{k!}}\left( {\frac{1} {2}\sigma ^2 } \right)^k ,kinteger $$
(2.1)
All odd moments are equal to zero.

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Copyright information

© Springer Science + Business Media, LLC 2002

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