# Question on Poisson processes

1. Aug 24, 2011

### Jösus

1. The problem statement, all variables and given/known data

Let $N(t)$ be a Poisson process with intensity $a$. Let $T$ be the occurrence of the first event in $(0,t]$ for some $t>0$, if there is such a one. If there are no events in $(0,t]$ we set $T=t$. Compute $E(T)$.

2. Relevant equations
None.

3. The attempt at a solution
I have no clue, but I would really appreciate some help.