Consider a set of n independenttrials in which there are r

Question

Let N be the r-dimensional random vector with the multinomial PMF given in Example 5.1 with n > r > 2:

(a) What is the joint PMF of N₁ and N₂?

(b) Let T_i = N₁ +···+ N_i. What is the PMF of T_i?

 (c) What is the joint PMF of T₁ and T₂?

Example 5.1

Consider a set of n independenttrials in which there are r possible outcomes s₁,...,s_r for each trial. In each trial, P[s_i] = p_i. Let N_i equal the number of times that outcome si occurs over n trials. What is the joint PMF of N₁,..., N_r?