Multinomial Distribution Formula. P knk where n n 1 n 2. N 1.
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. For any positive integer m and any nonnegative integer n the multinomial formula tells us how a sum with m terms expands when raised to an arbitrary power n. 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.
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.
We also say that y 1 y 2 ldots y k 1 has this distribution recall that the values of k 1 of the counting variables determine the value of the remaining variable. Probability and distributions formulas list online. Can be found by the following formula. P n.
