Editing Multivariate random variable (section)

==Probability distribution==
{{main|Multivariate probability distribution}}
Every random vector gives rise to a probability measure on <math>\mathbb{R}^n</math> with the [[Borel algebra]] as the underlying sigma-algebra. This measure is also known as the [[joint probability distribution]], the joint distribution, or the multivariate distribution of the random vector.

The [[Probability distribution|distributions]] of each of the component random variables <math>X_i</math> are called [[marginal distribution]]s. The [[conditional probability distribution]] of <math>X_i</math> given <math>X_j</math> is the probability distribution of <math>X_i</math> when <math>X_j</math> is known to be a particular value.

The '''cumulative distribution function''' <math>F_{\mathbf{X}} : \R^n \mapsto [0,1]</math> of a random vector <math>\mathbf{X}=(X_1,\dots,X_n)^\mathsf{T} </math> is defined as<ref name=Gallager>{{cite book |first=Robert G. |last=Gallager|year=2013 |title=Stochastic Processes Theory for Applications |publisher=Cambridge University Press |isbn=978-1-107-03975-9}}</ref>{{rp|p.15}}

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|equation = {{NumBlk||<math>F_{\mathbf{X}}(\mathbf{x}) = \operatorname{P}(X_1 \leq x_1,\ldots,X_n \leq x_n)</math>|{{EquationRef|Eq.1}}}}
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where <math>\mathbf{x} = (x_1, \dots, x_n)^\mathsf{T}</math>.