I am new here so if I violate any rule, please inform.
Consider the stochastic process given by $\{ N(t) : t \geq 0 \}$ which is time homogeneous poisson process with arrival rate $\lambda$. Let $W_n$ be the waiting time, i.e, $W_n = \inf \{t\geq0:N(t)=n \}$.
We want to show that $P(W_k < \infty) = 1 \ \ \forall k=1,2,\ldots $.
Any help would be appreciated.
Thanks.