Multinomial Distribution Mean And Variance Derivation. Hence the mean and variance of x i are np i and np i 1 p i respectively. The multinomial distribution is a generalization of the binomial distribution.
If you perform times an experiment that can have only two outcomes either success or failure then the number of times you obtain one of the two outcomes success is a binomial random variable. Thus x i j y i j. If k 2 the multinomial distribution becomes a binomial distribution with n trials and success probability p 1.
When x x 1 x 2 x k follows a multinomial distribution with the pmf given above x i follows a binomial distribution with n trials and success probability p i.
The following results are what came out of it. Because the binomial distribution is so commonly used statisticians went ahead and did all the grunt work to figure out nice easy formulas for finding its mean variance and standard deviation. If k 2 the multinomial distribution becomes a binomial distribution with n trials and success probability p 1. The following results are what came out of it.
