In Example 6.20, we computed m(t) =E[O(t)], the expected occupa- tion time in state 0 by time for the two-state continuous-time Markov chain starting in state 0.

Another way of obtaining this quantity is by deriving a differential equation for it.

(a) Show that m(t + h) = m(t) + Poo(!)h + o(h)

(b) Show that m'(1) = 2+1 2 + 1 +

(c) Solve for m(t).