We have two independent Poisson processes, Z1(t) and Z2(t), with respective parameters r and s. They are running parallel. If Y(t) is the process from the overlay of Z1(t) and Z2(t), show that Y(t) is also a Poisson process. What is the rate of Y(t)?
The following exercise demonstrates a method for showing that a process is a Poisson process. The rate of the process is computed as well.