In N Bernoulli trials, where N is a random variable with a Poisson distribution, the numbers of

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In N Bernoulli trials, where N is a random variable with a Poisson distribution, the numbers of successes and failures are stochastically independent variables. Generalize this to the multinomial distribution

(a) directly,

(b) using multivariate generating functions. [Cf. example IX,(1.d).]

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