# Poisson process: nth jump from expectation of interarrival time

The interarrival time for a poisson process is given as

$\Bbb E[T_i] = 1/\lambda$

How can I compute the arrival time for the $nth$ jump from this. Surely its not equal to $n/\lambda$ ?

• The mean is indeed $\frac{n}{\lambda}$. – André Nicolas Jun 15 '14 at 19:09

The mean value $E(t) = \frac{n}{\lambda}$ and dispersion $D = \frac{n}{\lambda^2}$