A rat is placed at random in one of the compartments of the maze pictured. The probability that a rat in compartment 1 will move to compartment 2 is 0.3; to compartment 3 is 0.2; and to compartment 4 is 0.1. A rate in compartment 2 will move to comparts 1, 4, or 5 with probabilities 0.2, 0.6, and 0.1, respectively. A rat in compartment 3 cannot leave that compartment. A rat in compartment 4 will move to 1, 2,3, or 5 with probabilities of 0.1, 0.1, 0.4, and 0.3, respectively. A rat in compartment 5 cannot leave that compartment.

a) Set up a transition matrix using this information. Find the matrices F and FR.

Find the probability that a rat ends up in compartment 5 if it was originally in the given compartment.

                        b) 1            c) 2           d)3           and           e)4

f) Find the expected number of times that a rat in compartment 1 will be in compartment 1 before ending up in compartment 3 or 5.

g) Find the expected number of times that a rat in compartment 4 will be in compartment 4 before ending up in compartment 3 or 5.