Suppose that you program the screen on your friendSolutionTr

Suppose that you program the screen on your friend

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.