The transition probability matrix of Markov Chain is

Find the limiting probabilities.

To find the limiting probabilities i.e $lim_{n→∞}⁡ {P^n}$

Let the limiting probabilities be π=[$π_1 π_2 π_3$ ]. Then we have πP=π such that $∑π_i=1$

∴[$π_1 π_2 π_3$ ]=[$π_1 π_2 π_3$ ]

$0.5π_1+0.3π_2+0.2π_3=π_1$ (1)

$0.4π_1+0.4π_2+0.3π_3=π_2$ (2)

$0.1π_1+0.3π_2+0.5π_3=π_3 $ (3)

We know$∑π_i=1$

$π_1+ π_2+ π_3=1$ (4)

i.e $ π_3=1-π_1-π_2$

Substituting the …