1. ## Probability Question

The following was confusing me so any help would be greatly appreciated!

P(N_i = n_i, i = 1,....,k) = n!/(n_1!n_2!...n_k!) * ((p_1)^(n_1))((p_2)^(n_2))....((p_k)^(n_k)) is known as the multinomial distribution.

Find the marginal distributions of the multinomial distribution.

2. Originally Posted by clockingly
The following was confusing me so any help would be greatly appreciated!

P(N_i = n_i, i = 1,....,k) = n!/(n_1!n_2!...n_k!) * ((p_1)^(n_1))((p_2)^(n_2))....((p_k)^(n_k)) is known as the multinomial distribution.

Find the marginal distributions of the multinomial distribution.
The marginal distribution of $N_i$ is the distribution of $N_i$ ignoring the information about $N_j,\ j \ne i$, and so is binomial (just by reinterpreting the definition multinomial distribution this should be obvious):

$
P(N_i=n_i) = \frac{n!}{n_i!,(n-n_i)!} p_i^n (1-p_i)^{n-n_i}
$

RonL