(The Yule Process) A cosmic particle entering the earth’s atmosphere collides with air particles and transfers kinetic energy to them. These in turn collide with other particles transferring energy to...

(The Yule Process) A cosmic particle entering the earth’s atmosphere collides with air particles and transfers kinetic energy to them. These in turn collide with other particles transferring energy to them and so on. A shower of particles results. Suppose that the time that it takes for each particle to collide with another particle is exponential with parameter λ. Find the probability that t units of time after the cosmic particle enters the earth’s atmosphere, there are n particles in the shower it causes.