Stationary Distribution in a 3×3 Markov Chain
Given the transition matrix: \(P = \begin{pmatrix}0.5 & 0.3 & 0.2 \\ 0.2 & 0.5 & 0.3 \\ 0.3 & 0.2 & 0.5\end{pmatrix}\) find the stationary distribution \(v = (v_1, v_2, v_3)\) such that \(v = vP\) and \(v_1 + v_2 + v_3 = 1\).