The same scenario is used for the remainder of the questions 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 $[1\mathrm{.}00\mathrm{.}00\mathrm{.}00\mathrm{.}00\mathrm{.}01\mathrm{.}00\mathrm{.}00\mathrm{.}0$ P $=0\mathrm{.}50\mathrm{.}00\mathrm{.}40\mathrm{.}10\mathrm{.}60\mathrm{.}10\mathrm{.}20\mathrm{.}1$