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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 Ti = N1 +···+ Ni. What is the PMF of Ti?
(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,...,sr for each trial. In each trial, P[si] = pi. Let Ni equal the number of times that outcome si occurs over n trials. What is the joint PMF of N1,..., Nr?
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