Categorical distribution

The $𝑛$ -dimensional categorical distribution is a generalization of the Bernoulli trial to multiple outcomes. Let $⃗ 𝐩 \in (ℝ +) 𝑛$ such that $\sum 𝑛 𝑗 = 1 𝑝 𝑖 = 1$ . We say $⃗ 𝐗 \sim C a t 𝑛 (⃗ 𝐩)$ iff $ℙ [⃗ 𝐗 = ˆ 𝐞 𝑖] = ⃗ 𝐩 \cdot ˆ 𝐞 𝑖$ , where $ˆ 𝐞 𝑖$ has 1 in the $𝑖$ th position and zeroes elsewhere. prob