Here is the question I meet.
Let $N = (N_t, t > 0)$ be a Poisson Process of rate $λ ∈ (0, ∞)$.
Show that for all $a ∈ (0, ∞)$ and $n ∈ N$,
$P(N_{na} < n) \leq (aλe^{1−λa})^n$
I found that when $n=1$, $P(N_{a} < 1) = e^{-λa}$.
Comparing to $aλe^{1−λa}$, I think the question is wrong.
Is there any problem in my process? Thanks.
Also, I was given the hint that combining mgf and Markov's inequality, but I have no idea how they are related.