# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 40: Multinomial Distribution

multinomial distribution is a generalization of the binomial distribution. Where an experiment with a binomial distribution has 2 outcomes, a multinomial experiment has $k$ outcomes, and where a binomial distribution gives the probabilities of exactly $m$ ‘successes’ out of $n$ experiments, a multinomial distribution gives the probabilities of all possible combinations of numbers of successes of the $k$ outcomes.

For instance, if one rolls a six-sided die $k$ times, the number of 1s, 2s, 3s, 4s, 5s, and 6s seen in those $k$ rolls follows a multinomial distribution.