17. Suppose that an experiment can result in one of r possible outcomes, the ith outcome having probability pi , i = 1, . . . , r,

ri

=1 pi = 1. If n of these experiments are performed, and if the outcome of any one of the n does not affect the outcome of the other n − 1 experiments, then show that the probability that the first outcome appears x1 times, the second x2 times, and the rth xr times is

This is known as the multinomial distribution.

Transcribed Image Text:

n! when x1 + x2 + + x = n x1!x2! xp!