# Operational Research probabilistic models

Recall the following definition of a Poisson process with rate ? > 0 : a counting process {N(t)} with N(0) = 0 is called a Poisson process with rate ? if the following are true: it has independent increments; and for each t > 0, N(t) is a Poisson random variable with parameter ?t. Using the above definition to show that, for each v, t > 0, N(t + v) ? N(t) follows Poisson distribution with parameter ?v. [20 marks]