Multinomial Formula. Obviously k 1 k 2 cdots k m n p 1 p 2 cdots p m 1. A b c a b c a b c a b c then apply the distributive law and then simplify by collecting like terms.
For any positive integer m and any non negative integer n the multinomial formula tells us how a sum with m terms expands when raised to an arbitrary power n. The number of times k i that the outcome i occurs is called its frequency. Question 1 out of 1.
Multinomial formula synonyms multinomial formula pronunciation multinomial formula translation english dictionary definition of multinomial formula.
Left x 1 x 2 cdots x k right n sum b 1 b 2 cdots b k n binom n b 1 b 2 b 3 ldots b k prod j 1 k x j b j. 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. A multinomial probability p refers to the probability of obtaining a specified set of frequencies in a multinomial experiment. Note that the binomial distribution is a special case of the multinomial when k 2.
