In Example 4f, we showed that the covariance of the multinomial random variables Ni and Nj...

In Example 4f, we showed that the covariance of the multinomial random variables Ni and Nj is equal to -mPiPj by expressing Ni and Nj as the sum of indicator variables. We could also have obtained that result by using the formula

(a) What is the distribution of Ni + Nj?

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(b) Use the preceding identity to show that Cov(Ni, Nj) = -mPiPj.