(1) FindX_{2}(the probability distribution of the system after two observations) for the distribution vectorX_{0}and the transition matrixT.

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]

findTX_{0}, the probability distribution of the system after one observation.

X_{1 }= ___

____

____