Question: 6. Let N(t) : t 0 be a Poisson process. For k 1, let Sk be the time that the kth event occurs.

6. Let

N(t) : t ≥ 0


be a Poisson process. For k ≥ 1, let Sk be the time that the kth event occurs. Show that

E[Sk | N(t) = n] kt n+1

E[Sk | N(t) = n] kt n+1

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