Question: 18. Let N(t) : t 0 be a Poisson process. For s < t show that the conditional distribution of N(s) given N(t)

18. Let

N(t) : t ≥ 0

be a Poisson process. For s < t show that the conditional distribution of N(s) given N(t) = n is binomial with parameters n and p = s/t. Also find the conditional distribution of N(t) given N(s) = k.

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