[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]

Write a program to simulate the outcomes of a Markov chain after [math]n[/math] steps, given the initial starting state and the transition matrix [math]\mat{P}[/math] as data (see Example). Keep this program for use in later problems.