Multinomial Distribution Formula. X 1 x 2 x m n k 1 k 2 k m n n k 1 k 2 k m t 1 m x t k t displaystyle x 1 x 2 cdots x m n sum k 1 k 2 cdots k m n n choose k 1 k 2 ldots k m prod t 1 m x t k t. Note that the binomial distribution is a special case of the multinomial when k 2.
We can also use a range as the argument of multinomial as in figure 1. For n independent trials each of which leads to a success for exactly one of k categories with each category having a given fixed success probability the multinomial distribution gives the. P knk where n n 1 n 2.
The distribution of bs y y 1 y 2 ldots y k is called the multinomial distribution with parameters n and bs p p 1 p 2 ldots p k.
N 2 2 number won by player b n 3 3 the number drawn p 1 0 40 probability player a wins p 2 0 35 probability player b wins p 3 0 25 probability of a draw the formula for k outcomes is. X 1 x k thus we could also calculate the answer to example 9 10 by using the formula. Probability and distributions formulas list online. If a random variable x follows a multinomial distribution then the probability that outcome 1 occurs exactly x1 times outcome 2 occurs exactly x2 times outcome 3 occurs exactly x3 times etc.
