A firm classifies its stockbrokers in four categories: Poor, Below Average, Good, Very Good, and Excellent. If a broker is classified as poor, they will be fired (and always hold the poor stock- broker classification). If a broker is classified as below average, they will be placed in a different department (and always hold the below average stock-broker classification). Stockbrokers who are rated as Excellent will be promoted to team leader (and always hold the excellent stock- broker classification). Stockbrokers classified as Good or Very Good may see their status change according to the following probabilities: Prob. Poor Below Avg Good Very Good Excellent
Good 0.1 0.1 0.55 0.2 0.05
Very Good 0.02 0.1 0.5 0.25 0.13
Find the steady-state probabilities for reaching the absorbing states from each non-absorbing state.