This is a Markov chain {Xn, n >= 0} with state space E = {1,2,3} The transition matrix P is
.2 .5 .3
.2 0 .8
.3 .1 .6
The initial distribution vector is p(0) = (0,1,0).
How do I calculate these?
Pr{X3 = 3 given that X1 = 1}
Pr{X3 in {2,3} given that X1 = 1}
Pr{X2 = 1, X3 = 2}