[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Using the program MatrixPowers, find [math]\mat {P}^1[/math] through [math]\mat {P}^6[/math] for Example and example. See if you can predict the long-range probability of finding the process in each of the states for these examples.