# Probability Distributions and Generating Functions

• Jon Wakefield
Chapter
Part of the Springer Series in Statistics book series (SSS)

## Abstract

The p-dimensional random variable $$X = {[{\textbf{X} }_{1},\ldots,{X}_{p}]}^{\mbox{ T}}$$ has a normal distribution, denoted $${\mbox{ N}}_{p}(\boldsymbol\mu,\boldsymbol\Sigma )$$, with mean $$\boldsymbol\mu = {[{\mu }_{1},\ldots,{\mu }_{p}]}^{\mbox{ T}}$$ and p ×p variance–covariance matrix $$\Sigma$$ if its density is of the form
$$p(\textbf{x} ) = {(2\pi )}^{-p/2}\mid \boldsymbol\Sigma {\mid }^{-1/2} \times \exp \left [-\frac{1} {2}{(x-\mu )}^{\mbox{ T} }{\boldsymbol\Sigma }^{-1}(x-\boldsymbol\mu )\right ],$$
for $$\textbf{} x \in {\mathbb{R}}^{p}$$, $$\boldsymbol\mu \in {\mathbb{R}}^{p}$$ and non-singular $$\boldsymbol\Sigma$$.

## Keywords

Probability Density Function Gamma Distribution Marginal Distribution Random Matrix Beta Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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