1. Let Xt be a discrete time Markov chain defined on ={0,1,2} for t=0,1,2,. The transition probability of Xt is stationary and pij=P{Xt+1=jXt=i} represents the transition probability for i and j. The transition probability matrix is as follows: P=p00p10p20p01p11p21p02p12p22=0.20.40.60.30.50.30.50.10.1 a) Calculate P{Xt+2=2Xt=0}. (10 points) b) Let ={0,1,2}. If a distribution satisfies =P, the is called the steady state distribution Xt. Find the steady state distribution. (20 points