Help please?

Question

Find the vector of stable probabilities for the Markov chain whose transition matrix is

.7 .3 0
0 0 1
1 0 0

Answer 1

You have three states. Probabilities of being in one of these states are x1, x2, x3. Therefore your vector (call it) |P| = |x1 x2 x3|. If we denote your transition matrix |T| then Markov chain balance equation is |P| = |P|*|T| plus the condition that you must be in one state x1+x2+x3=1. That gives a system of linear equations: x1 = 0.7*x1 + x3, x2 = x1*0.3, x3 = x2. When you solve it you get state probabilities: x1 = 1/1.6, x2 = x3 = 0.3/1.6.