Suppose we label the spaces on a monopoly board as {0, 1, 2… 39} where,
0 = Go,
1 = Mediterranean Ave.,
2 = Community Chest,
3 = Baltic Ave.,
...
39 = Boardwalk.
Let X [k] be the location of a player after k turns. On each turn, a player moves by rolling two (six- sided) dice and moving forward the number of places indicated by the sum of the two dice. Any time the roll of the dice causes the player to land on space 30 (Go to Jail) the player’s token is immediately moved to space 10 (Jail). Describe the elements of the transition probability matrix, pi,j, for the monopoly Markov chain X [k].