Assume that calls arrive at a call center according to a Poisson arrival process with a rate of λ calls per hour. For $0 <= s < t$, what is the probability of $N((0,s]) = m$, when conditioned on the event $N((0,t]) = n$ (assume $n >= m$)?
I know the formula for a Poisson distribution. And I think that $E(N((0,s])) = s\cdot λ$.
I'm not sure how to work with this information though.
Any hints are greatly appreciated!