Let N1 , N2 , N3 follow a trinomial distribution with parameters
n, assume that n...
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Let N1 , N2 , N3 follow a trinomial distribution with parametersn, assume that n follows a Poisson distribution with parameter λ> 0. Also assume that, conditionally on N, the random variablesN1, N2, N3 follow a trinomial distribution with N trials andcategory probabilities p1, p2, p3 with p1 + p2 + p3 = 1. Computethe covariance and correlation of (N1,N2)
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The pmf of multinomial random variable is defined aswhereThis is
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