Robots have been programmed to traverse the maze shown in Figure 3.28 and at each juncti...

Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go.

(a) Construct the transition matrix for the Markov chain that models this situation.

(b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)