# Question: Let Xi t i 1 2 n be a

Let, Xi (t) i = 1, 2… n, be a sequence of independent Poisson counting processes with arrival rates,λi. Show that the sum of all of these Poisson processes,

Is itself a Poisson process. What is the arrival rate of the sum process?

Is itself a Poisson process. What is the arrival rate of the sum process?

## Answer to relevant Questions

A workstation is used until it fails and then it is sent out for repair. The time between failures, or the length of time the workstation functions until it needs repair, is a random variable T. Assume the times between ...Consider a Poisson counting process with arrival rate, λ. Suppose it is observed that there have been exactly arrivals in [0, t] and let S1, S2… Sn be the times of those arrivals. Next, define X1, X2… Xn to be a ...Let N (t) be a Poisson counting process with arrival rate, λ. Determine whether or not N (t) is mean square continuous. Find the PSD of the process described in Exercise 8.1. For a Markov chain, prove or disprove the following statement: Pr (Xk = ik | Xk + 1 = ik + 1, Xk + 2 = ik + 2… Xk+ m = ik+ m) = Pr (Xk = ik | Xk + 1 = ik + 1) Suppose a process can be considered to be in one of two states (let’s call them state A and state B), but the next state of the process depends not only on the current state but also on the previous state as well. We can ...Post your question