[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]

If [math]\mat{P}[/math] is a reversible Markov chain, is it

necessarily true that the mean time to go from state [math]i[/math] to state [math]j[/math] is equal to the mean time to go from state [math]j[/math] to state [math]i[/math]? Hint: Try the Land of Oz example (Example).