# Multinomial Distribution

The joint pmf is given by $f(x_{1},x_{2},β¦,x_{n})=x_{1}!x_{2}!β¦x_{n}!n!βp_{1}p_{2}β¦p_{n}$

Marginals $f_{x_{1}}(x_{1})=(x_{1}nβ)p_{1}(p_{2}+β―+p_{n})_{x_{2}+β―+x_{k}}$

Conditionals I a little iffy about what this means, they gave this example, but I donβt think itβse worthy to put it in my notes.

### PyTorch

Serendipity learned this from STAT206, and now I am applying it from Andrej Karpathy.

We use the probability distribution to generate a tensor of indices.