(1) Find X_{2} (the probability distribution of the system after two observations) for the distribution vector X_{0} and the transition matrix T.
X_{o }= [1/6]
[5/6]
[ 0 ]
T= [1/2 1/3 1/2]
[0 1/3 1/4]
[1/2 1/3 1/4]
X_{2} = ______
______
______
(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]
X_{o}=
State 2 [4/5]
find TX_{0}, the probability distribution of the system after one observation.
X_{1 }= ___
____
____