A one-celled organism can be in one of two states - either A or B. Any individual in state A will change to an individual in state B at an exponential rate α; any individual in state B will divide into two individuals, one of type A and one of type B, at an exponential rate β. The population can be modelled by a two-dimensional continuous-time Markov chain (Xt​,Yt​) where Xt​ is the number of individuals in state A and Yt​ is the number of individuals in state B, at time t. The states then consist of (i,j),i,j=0,1,… Explain which transitions are possible in the model, give the transition rates for the possible transitions, and draw the transition diagram. Show in your diagram the states (i,j) with i,j=0,1,2,3.