Question

Question 4 A shown at right. A random walker on G has transition probabilities to and from vertex 1 equal to /4, and all other transition to probabilities equal to 3/s. Let G be the digraph with adjacency matrix 0 1 1 1 1 1010 1 1 1010 A= 1 010 1 11010 (a) Draw the graph and mark on it the transition probabilities. (b) Compile the transition matrix T and verify that it is stochastic. (c) On average over the long term, what proportion of time will the walker spend Hint: There are really only two unknowns at vertex 1?

Answer 1

matrix A = The iven states m,2 ,3 the et 3/8 3/8 3/9 3/8 3/8 ム Transition matrix 2 Yム ソム 2/6 2 2/9 4 /9 and -getive mom- T eutries of Simce each to ro W each Bum of stochastic matix So, the matrix T