Determining the Steady State of a 2×2 Markov Chain
Given the 2×2 transition matrix \(P = \begin{pmatrix}0.8 & 0.2\\0.3 & 0.7\end{pmatrix}\) of a Markov chain, find the steady state vector corresponding to the eigenvalue \(\lambda = 1\). Recall that the steady state vector \(p = (p_1, p_2)\) satisfies \(p = Pp\) along with the constraint \(p_1 + p_2 = 1\).