How Is E(S5) Calculated in a Poisson Process?

[CTK]

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

 

[PeroK]

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.