A multinomial distribution arises when there are \(g\) possible outcomes from each of the \(n\) independent trials. We now concentrate on the number of times that one of these values is observed — its marginal distribution.
Marginal distributions
If \((X_1, X_2,\dots, X_g)\), have a \(\MultinomDistn(n, \pi_1, \dots, \pi_g)\) distribution, then the marginal distribution of any \(X_i\) is \(BinomDistn(n, \pi_i)\).
(Proved in full version)