Answer Happy

Suppose there is a system which behaves as follows. At time t = 0, there is a single particle, which we refer to as belonging to generation 0. This particle has an exp (1) clock. After the clock expires, the particle disintegrates and 2 new particles are created. Each of these particles has their own exp (1) clock. Whenever, either of these particle's clock's go off, that particle splits into two new particles, each of which gets its own new exp (1) clock. However, the other particles do not split at this time. There are then 3 particles, and the process continues on and on in this manner. For each t > 0, let X(t) denote the number of particles which exist at time t. Model X = {X(t). t>0} as a CTMC, specifying the underlying DTMC transition matrix, the underlying rates, and the starting state.