Consider n independent trials each of which results in any o

Consider n independent trials, each of which results in any of the outcomes i, i = 1, 2, 3 with respective probabilities p1, p2, p3 such that p1 + p2 + p3 = 1. Let Ni denote the number of trials that result in outcome i, and show that Cov(N1,N2) = np1p2. Also explain why it is intuitive that this covariance is negative.

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