Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Transition Matrix

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data

    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.


    2. Relevant equations

    3. 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.
     

    Attached Files:

  2. jcsd
  3. Nov 29, 2012 #2
    Ok, I think I have it. The transition matrix should be:
    [.3 .7]
    [.4 .6]
    Right?
     
  4. Nov 29, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You can answer that for yourself. Does it change [0 1] into [.4 .6]? Does it leave [4/11,7/11] unchanged?
     
  5. Nov 29, 2012 #4
    It does. Thanks
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook