Find the steadystate matrix of 08 02 02 08 SolutionTP 08020

Find the steady-state matrix of

	0.8	0.2
0.2	0.8

Solution

TP = {{0.8,0.2},{0.2,0.8}}*{{x},{y}}
= {{0.8x + 0.2y},{0.2x + 0.8y}}
TP = P =>{{0.8x + 0.2y},{0.2x + 0.8y}} = {{x},{y}}
0.8x + 0.2y = x => y = x
0.2x + 0.8y = y =>x = y
So from the equation TP = P, we have
x = y-----------------------------------------------------------       (1)
Since P is a probability distribution, we should have:
x + y = 1 --------------------------------------------------------(2)
From
(1) , (2) => x + x = 1 => x = 1/2 => y = x = 1/2
Therefore the steady state probability column matrix is:
P = ((