Particles enter a chamber through two openings at the left as shown in the figure. Arrival process at each opening is Poisson with intensity = 2 per unit time. Particles move with constant velocity v = 5 millimeters per unit time in the chamber and exit at the opening at the right. The length of the chamber is 100 millimeters. Once in the chamber, each particle has a lifetime that is exponentially distributed with parameter = 0.1. At the end of its lifetime, the particle decays into pure energy. Let X(t) be the departure process of the particles at the right opening of the chamber.

(a) Show that X(t) is Poisson

(b) Find the intensity of the process X(t).