The point of this exercise is to show that the sequence of PMF’s for a Bernoulli counting process does not specify the process. In other words, knowing that N(t) satisfies the binomial distribution...

The point of this exercise is to show that the sequence of PMF’s for a Bernoulli counting process does not specify the process. In other words, knowing that N(t) satisfies the binomial distribution for all t does not mean that the process is Bernoulli. This helps us understand why the second definition of a Poisson process requires stationary and independent increments as well as the Poisson distribution for N(t).