[[Multivariate random variable]]
# Categorical distribution

The $n$-dimensional **categorical distribution** is a generalization of the [[Bernoulli trial]] to multiple outcomes.
Let $\vab p \in (\mathbb{R}^+)^n$ such that $\sum_{j=1}^n p_{i} = 1$.
We say $\vab X \sim \mathrm{Cat}_{n}(\vab p)$ iff $\mathbb{P}[\vab X = \unitv e_{i}] = \vab p \cdot \unitv e_{i}$,
where $\unitv e_{i}$ has 1 in the $i$th position and zeroes elsewhere. #m/def/prob 


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