The multinomial distribution more than one kind of success

The multinomial distribution is an extension of the binomial distribution to the case of more than two (we shall assume n) kinds of outcomes, in which a single trial has probability p, of ending in category i. In a total of N trials, we assume that k, of the outcomes end in category i. If we let p denote the vector of the different probabilities of outcome and k denote the vector of the data, the probability distribution is then an extension of the binomial distribution

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