# Question

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

Var(Ni + Nj) = Var(Ni) + Var(Nj) + 2 Cov(Ni, Nj)

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

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

Var(Ni + Nj) = Var(Ni) + Var(Nj) + 2 Cov(Ni, Nj)

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

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

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