[[Real random variable]]
# Multivariate random variable

A **multidimensional random variable** allows multiple [[Real random variable|real random variables]] in the same [[Probability model|event space]] to be treated together.
$$
\begin{align*}
\vab X = \tp{[X_{1}, X_{2}, \dots , X_{n}]}: \xi \to \mathbb{R}^n
\end{align*}
$$
The probability distribution is then described by the [[Joint cumulative distribution function]], and the
[[Joint probability density function]] or [[Joint probability mass function]] (depending on whether the underlying variables are continuous or discrete).

## Examples

- [[Multinomial distribution]]
- [[Multivariate normal distribution]]

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#state/tidy | #lang/en | #SemBr