Super positions of Renewal Processes. Let N1(t) and N2(t) be independent renewal processes with the same inter-renewal distribution, and consider the sum N(t) = N1(t) + N2(t) (sometimes called a...

Super positions of Renewal Processes. Let N1(t) and N2(t) be independent renewal processes with the same inter-renewal distribution, and consider the sum N(t) = N1(t) + N2(t) (sometimes called a superposition). Assuming that N(t) is a renewal process. prove that it is a Poisson process if and only if N1(t) and N2(t) are Poisson processes.