Multinomial Distribution

  This is an extension of the binomial distribution to the case where there are more than two classes into which an event can fall. The most common example is a histogram containing N independent events distributed into n bins. Then if p_i is the probability of an individual event falling in the ith bin, the probability of exactly r_i events falling in bin i for each i is:

where

The expectation value, variance, correlation coefficient of the r_i are:

Even though the events are independent, there is a correlation between bin contents because the sum is constrained to be N.