Reference no: EM132438005

Seven boys are playing with a ball. The first boy always throws it to the second boy. The second boy is equally likely to throw it to the third or seventh. The third boy keeps the ball if he gets it. The fourth boy always throws it to the sixth. The fifth boy is equally likely to throw it to the fourth, sixth or seventh boy. The sixth boy always throws it to the fourth. The seventh boy is equally likely to throw it to the first or fourth boy?

a) Set up the transition matrix P.

b) Classify the states.

c) Give an interpretation for the chain ending up in one of the ergodic sets.

Suppose the process below in Figure 1 starts in state 2. What is the mean number of times it visits state 2?