Answer Happy

Suppose that an experiment can result in one of r possible outcomes, the ith outcome having probability Pi, i = 1, ..., r, Si=1 Pi = 1. If n of these experi- ments 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 xy times is n! p" when x1 + x2 +...+ xy =n Xı! x2!...x,! P39p2...po This is known as the multinomial distribution. In Exercise 17, let X; denote the number of times the ith outcome appears, i=1, ..., r. What is the probability mass function of X1 + X2 + ... + Xk?