The US Army Hires Only Newly Minted Graduates for a Special

Essay

The U.S. army hires only newly minted graduates for a special officer program. They always start on January 1 and are considered for promotion every January 1st thereafter. On January 1st, existing officers (state O) - those who were officers last year-may continue as officers, be promoted to manager cadres (state M), retire (state R ), or be dead while in service (state D). Everyone in state M on January 1st may continue in state $\mathrm{M}$ or move to states $\mathrm{R}$ or $\mathrm{D}$ . Using the data from the transition matrix and using 1 year as the transition time, calculate the probability of an officer eventually being retired or dead while in service. Similarly, calculate the probability of a manager eventually being retired or dead while in service.