Problem #$3$: Suppose that a Markov chain has the following transition matrix, which you can copy and paste directly into

Matlab.

$A=\{\begin{array}{ccc}\text{:}[0\mathrm{.}2851,& 0\mathrm{.}2989,0\mathrm{.}1172,0\mathrm{.}4016,0\mathrm{.}2936\text{;}0\mathrm{.}1773,0\mathrm{.}0205,0\mathrm{.}2091,& 0\mathrm{.}3244]\end{array}$

$\{\begin{array}{ccc}\text{:}[0\mathrm{.}1381\text{;}0\mathrm{.}2207,& 0\mathrm{.}2989,0\mathrm{.}3048,0\mathrm{.}113,0\mathrm{.}241\text{;}0\mathrm{.}1946,0\mathrm{.}2993,0\mathrm{.}232,& 0\mathrm{.}0902]\end{array}$

$0\mathrm{.}1993$;$0\mathrm{.}1224,0\mathrm{.}0825,0\mathrm{.}1369,0\mathrm{.}0708,0\mathrm{.}128$

Find the steady state vector and use it to determine the proportion of time $($in the long run$)$ that the process spends

in State $4.$

Problem #$3$:$0\mathrm{.}19999659070001216$

Submit Problem #$3$ for Grading