Let Yk be the time of the k th arrival in a Poisson process with parameter λ=1 . In particular, E[Yk] = k .

Question

1. Is it true that P(Yk≥k) = 1/2 for any finite k ?

2. Is it true that limk→∞P(Yk≥k) = 1/2 ?

Answer 1

1. No
2. Yes