[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]

Modify the program of Exercise Exercise so

that it keeps track of the proportion of times in each state in [math]n[/math] steps. Run the modified program for different starting states for Example and Example. Does the initial state affect the proportion of time spent in each of the states if [math]n[/math] is large?