A certain type of component has two states: 0 = OFF and 1 = OPERATING. In state 0 , the process remains there an exponential amount of time with rate $ \alpha$, and then moves to state 1. The component spends an exponential amount of time with rate $\beta$ in state 1 after which the process returns to state 0. A system consists of two such components A and B. Assume that the amounts of time the components spend in the states are independent of one another and have rates given by the following.
$$\begin{array}{c|c|c|} & \text{Off Rate($\alpha$)} & \text{Operating Rate($\beta$)} \\ \hline \text{A} & 2 & 4 \\ \hline \text{B} & 3 & 6 \\ \hline \end{array}$$
Consider the continuous Markov chain with states ${0,A,B,2}$ representing the component currently operating. Enumerate the transition rates $v_i$ and the transitional probabilities $p_ij$.
My transition rates are $v_0 = 2, v_A =1, v_B =3, v_2 = 3 $. Is my answer right?How do I get the transitional probabilities? Thanks a lot.