[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]

Which of the following matrices are transition matrices for regular Markov chains?

• [math]\mat {P} = \pmatrix{ .5 & .5 \cr .5 & .5 }[/math]
• [math]\mat {P} = \pmatrix{ .5 & .5 \cr 1 & 0 }[/math]
• [math]\mat {P} = \pmatrix{ 1/3 & 0 & 2/3 \cr 0 & 1 & 0 \cr 0 & 1/5 & 4/5}[/math]
• [math]\mat {P} = \pmatrix{ 0 & 1 \cr 1 & 0}[/math]
• [math]\mat {P} = \pmatrix{ 1/2 & 1/2 & 0 \cr 0 & 1/2 & 1/2 \cr 1/3 & 1/3 & 1/3}[/math]