Chapter 2.5, Problem 29E

Regular and Steady State Matrices In Exercises $17-30$, determine whether the stochastic matrix $P$ is regular. Then find the steady state matrix $\bar{X}$ of the Markov chain with matrix of transition probabilities $P$ .

$P=\left[\begin{array}{cccc}\frac{1}{4}& \frac{1}{3}& \frac{1}{2}& 1\\ \frac{1}{4}& \frac{1}{3}& \frac{1}{2}& 0\\ \frac{1}{4}& \frac{1}{3}& 0& 0\\ \frac{1}{4}& 0& 0& 0\end{array}\right]$