Multinomial Formula. Note that the binomial distribution is a special case of the multinomial when k 2. 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.
It can be expressed by the following formula. Multinomial theorem for a positive integer k k k and a non negative integer n n n x 1 x 2 x k n b 1 b 2 b k n n b 1 b 2 b 3 b k j 1 k x j b j. Where the numberarguments are one or more integers or arrays of integers for which you want to calculate the multinomial.
Is the factorial notation for 1 2 3 n.
In probability theory the multinomial distribution is a generalization of the binomial distribution for example it models the probability of counts for each side of a k sided die rolled n times. The number of times k i that the outcome i occurs is called its frequency. In particular the expansion is given by where n 1 n 2 n k n and n. A b c a b c a b c a b c then apply the distributive law and then simplify by collecting like terms.
