Solving Transition Matrix Homework Statement

[alexcc17]

Homework Statement

The problem is in the attachment, but I'll try and rewrite it...

Suppose for a Markov Chain with two states, we get the following results.
1. If P0=[0 1] then P1=[.4 .6]

2. If P0=[4/11 7/11] then P0=P1=P2=...and so on.

With this information, find the transition matrix of the Markov process.

Homework Equations

The Attempt at a Solution

I'm a bit confused here. The second part means that P0=[4/11 7/11] never changes, so the transition matrix does nothing and it is a stable vector, but doesn't the transition matrix have to do something because it in #1 it changes the matrix from P0 to P1?

So... T * [4/11 7/11]=[4/11 7/11] and T*[0 1]=[.4 .6]

Any help would be great.

 

[alexcc17]

Ok, I think I have it. The transition matrix should be:
[.3 .7]
[.4 .6]
Right?

 

[Ray Vickson]

Ok, I think I have it. The transition matrix should be:
[.3 .7]
[.4 .6]
Right?

You can answer that for yourself. Does it change [0 1] into [.4 .6]? Does it leave [4/11,7/11] unchanged?

 

[alexcc17]

It does. Thanks