Definition 8.1.1. Poisson Process.

Consider an experiment that takes place over some interval of time. A Poisson process is a course of action in which:
  1. Successes in non-overlapping subintervals are independent of each other.
  2. The probability of exactly one success in a sufficiently small interval of length h is proportional to h. In notation, P(one success) = \(\lambda h\text{.}\)
  3. The probability of two or more successes in a sufficiently small interval is essentially 0.
in-context