A random experiment takes r possible values, with respective probabilities p 1 , . . . ,p
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A random experiment takes r possible values, with respective probabilities p1, . . . ,pr. Suppose the experiment is repeated N times, where N has a Poisson distribution with parameter λ. For k = 1, . . . ,r , let Nk be the number of occurrences of outcome k. In other words, if N = n, then (N1, . . . ,Nr) has a multinomial distribution.
Show that N1, . . . ,Nr form a sequence of independent Poisson random variables and for each k = 1, . . . ,r, Nk ∼ Pois(λpk).
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