# Inter-arrival times problem

CTK
Thread moved from the technical forums to the schoolwork forums
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

Homework Helper
Gold Member
2022 Award
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 ##?
Why would that be the answer?

CTK
Why would that be the answer?
Hi PeroK. I guess I have just figured it out, so no worries. Thanks for your reply.