[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 result of Exercise, make a conjecture for the form of the fundamental matrix if the process moves as in that exercise, except that it now moves on the integers from 1 to [math]n[/math]. Test your conjecture for several different values of [math]n[/math]. Can you conjecture an estimate for the expected number of steps to reach state [math]n[/math], for large [math]n[/math]? (See Exercise for a method of determining this expected number of steps.)