Chapter 8, Problem 16RE

To determine

To calculate: The expected number of months spent in state G or S before being absorbed into state C or L by using fundamental matrix when the state of persons health is “able to work and considered cured (C) or “long-term hospitalization or death (L),”or “group home (G)” or short-term hospital care (S)” and the stochastic matrix which describes the transitions from month to month is shown below as,

$\begin{array}{l}\begin{array}{cccc}C& L& G& S\end{array}\\ \begin{array}{c}C\\ L\\ G\\ S\end{array}\left[\begin{array}{cccc}1& 0& 0.60& 0.05\\ 0& 1& 0.10& 0.40\\ 0& 0& 0.20& 0.50\\ 0& 0& 0.10& 0.05\end{array}\right]\end{array}$