Marked Poisson processes

Abstract

Abstract It was noted in Section 1.2 that the Poisson distribution has a characteristic property in relation to the binomial distribution. If the random variable N has distribution p(µ) and if a second random variable M has a conditional distribution, given N, of the form B(N, p), then M and N - M are independent Poisson variables, with respective means pµ and (1- p )µ.