Random Processes - 09 - Poisson Process Properties (Part 1)

We derive the probability mass function of the Poisson random process. This derivation uses properties of the underyling random sequences tau[n] and T[n] (i.e. the fact that they are independent) to derive an expression for P(N(t) = n). Not surprisingly, this expression is just the probability distribution of a Poisson random variable. This makes it almost trivial to determine the mean function and variance function of the Poisson random process.

[thehardlife]

Lets say you translated the poisson distribution and said what is the probability of when a person starts watching after t=10 what is the probability distribution of interarrival time T, of the first arrival after t =10