Definition:Random Vector

Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\struct {S, \Sigma'}$ be a measurable space.

Let $X_1, X_2, \ldots, X_n$ be random variables on $\struct {\Omega, \Sigma, \Pr}$ taking values in $\struct {S, \Sigma'}$.

Define a function $\mathbf X : \Omega \to S^n$ by:


 * $\map {\mathbf X} \omega = \tuple {\map {X_1} \omega, \map {X_2} \omega, \ldots, \map {X_n} \omega}$

for each $\omega \in \Omega$.

We call $\mathbf X$ a random vector.

Also known as
A random vector is also known as a multivariate random variable.

Also see

 * Random Vector is Random Variable