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**Summary:**inter-arrival times problem

Let {X(t) : t ≥ 0} be a Poisson process with rate λ.

a-) Let Si denote the time of the ith occurrence, i = 1, 2, . . . . Suppose it is known that X(1) = 5. Find ## E(S_{5}) ##.

My attempt: Is the answer simply ## n / \lambda = 5 / \lambda ##? Or is there more to it that I am missing?

Thanks for the help