Reflecting random walk on the line. Consider the points 1; 2; 3; 4 to be marked on a straight line. Let Xn be a Markov chain that moves to the right with probability 2=3 and to the left with probability 1=3, but subject this time to the rule that if Xn tries to go to the left from 1 or to the right from 4 it stays put. Find (a) the transition probability for the chain, and (b) the limiting amount of time the chain spends at each site