Question

You are given a transition matrix P. Find the steady-state distribution vector. HINT [See Example 4.]

P = [0.6 0 0.4

1 0 0

0 0.2 0.8]

Answer 1

In markov process the process starts from one of the set and moves succesively from one of the set to another set. There transtition from one set to another is always represented in form of transition probability matrix. Steady state is one which only depends on the process and staisfies condition given below

Let P be a transition probability matrix and X is a steady-state distribution, then for steady-state we have

Condition- PX=X

We have given transition matrix of order 3 given below

For steady state, we have PX=X, so we get

Therefore, we have three equation as

1. 0.6*x+0.4*z=x

2. 1*x=y

3. 0.2*y+0.8*z=z

Soving (1), we have

From equation (2), we have x=y.

From equation (3), we have

Therefore we have [x, y, z] or [x, x, x] as the steady state distribution but this steady-state distribution is not unique so we obtain its normal form as

Therefore, the steady-state distrivution vector is