A psychiatrist clinic classifies its accounts receivable into the following four states

State $1.$ Paid

State $2.$ Bad debt

State $3.0-30$ days

State $4.31-90$ days

The clinic currently has $$8000$ accounts receivable in the $0-30$ days state and $$2000$ in the $31-90$ days state. Based on historical transition from week to week of accounts receivable, the following matrix of transition probabilities has been developed for the clinic