Recall the following definition of a Poisson process with rate > 0 : a counting process {N(t)} with N(0) = 0 is called a

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