Suppose we want to know the average (or expected) number of steps it will take to go from state i to state j in a Markov chain. It can be shown that the following computation answers this question: Delete the jth row and the jth column of the transition matrix P to get a new matrix Q. (Keep the rows and columns of Q labeled as they were in P.) The expected number of steps from state i to state j is given by the sum of the entries in the column of

(I Q)¹

labeled i.

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

Starting from each of the other junctions, what is the expected number of moves until a robot reaches junction 1? (Round your answers to two decimal places.

A figure with 4 junctions and 6 paths is shown.

• Junction 1 is connected to junction 2 and junction 3.
• Junction 2 is connected to junction 1, junction 3, and junction 4.
• Junction 3 is connected to junction 1, junction 2, and has two paths connecting to junction 4.
• Junction 4 is connected to junction 2, and has two paths connecting to junction 3.