Poisson Process

Random events in time — the memoryless arrival process

Parameters

Poisson process:
P(N(t)=k) = e^(−λt)(λt)^k / k!

Inter-arrival times ~ Exp(λ):
f(x) = λe^(−λx)

Memoryless property:
P(T>s+t|T>s) = P(T>t)

Mean = Var = λt (equidispersion is the hallmark of the Poisson).
Mean count:
Var count:
λT (theory):