# Math Help - Markov Chain questions

1. ## Markov Chain questions

(1) Find X2 (the probability distribution of the system after two observations) for the distribution vector X0 and the transition matrix T.

Xo = [1/6]
[5/6]
[ 0 ]
T= [1/2 1/3 1/2]
[0 1/3 1/4]
[1/2 1/3 1/4]

X2 = ______
______
______

(2) Find the steady-state vector for the transition matrix.

[5/7 4/7]
[2/7 3/7]

X= _____
_____
_____

(3) Find the steady-state vector for the transition matrix.

[.6 .1 0 ]
[.4 .8 .6]
[0 .1 .4]

X= ___
___
___

(4)The transition matrix for a Markov process is given by
1 2
State 1 [1/3 5/6]
7=
State 2 [2/3 1/6]

(a) Given that the outcome state 1 has occurred, what is the probability that the next outcome of the experiment will be state 2?

(b) If the initial-state distribution is given by

State 1 [1/5]
Xo=
State 2 [4/5]

find TX0, the probability distribution of the system after one observation.

X1 = ___
____
____