On the other hand, a Poisson process is a memoryless stochastic point process; that an event has just occurred or that an event hasn't occurred in a long time give us no clue about the likelihood that another event will occur soon.

Which distributions are memoryless?

Only two kinds of distributions are memoryless: geometric distributions of non-negative integers and the exponential distributions of non-negative real numbers.

Why is Poisson not memoryless?

1 Answer. Memorylessness is a property of the following form: Pr(X>m+n∣X>m)=Pr(X>n) . This property holds for X1= time to the next event in a Poisson process , but it doesn't hold for Xk= time to thekthevent in a Poisson process when k>1.