Question: 38. In Example 6.20, we computed m(t) = E[0(t)], the expected occupation time in state 0 by time t for the two-state continuous-time Markov chain

38. In Example 6.20, we computed m(t) = E[0(t)], the expected occupation time in state 0 by time t 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) + P00(t)h + o(h)

(b) Show that

(c) Solve for m(t).

m\t) = - ^ - + -^—e-^)t

ë + ì ë + ì

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