Suppose that you program the screen on your friend Solution Transition matrix P is on 0.3 0.7 off 0.6 0.4 b) Let us find eigen values and eigen vector for P Eigen values are -0.3, 1 Eigen vectors are (-0.759, -0.707) and (0.652,-0.707) Spectral radius = 1 b) P^3 = 0.496 0.553 0.474 0.400 c) As 0.3 <1 we get P^n in the long run will have domination by 1. p^n = 1 (0.652, -0.707) Hence as 0.707>0.652, off most of time is the answer..