please answer the question with all the step. thank you

8. Suppose that {N1 (t) : t 2 0} and {N2 (t) : t 2 0} are independent Poisson processes with respective rates A1 and A2. Also dene a new process {N(t) : t 2 0} by N(t) = N1(t) + N2(t). You may use the fact, that you proved in question 5, that {N(t) : t 2 0} is a Poisson process with rate A1 | A2. Denote the corresponding waiting time sequences for the three processes by 8%\