Suppose {X(t): t E [0, o)} is a CTMC, with state space {1,2,3,4,..}, the transition probabilities are given by j=1 j=0 bit + o(at) Pi+j,i = Prob{X(t + At) X(t) = j|X(t) = i} = 1-bAt + o(At) (t) 0 = 6. For At sufficiently small. Suppose X(0) = 1, bo = 0, b = 1, b = 3 and b3 a. Write down the differential equations satisfied by p (t), p (t) and p3 (t). b. Solve the DE in (a). j2 j