Results 1 to 1 of 1

Math Help - Mean recurrence time

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    164

    Mean recurrence time

    Hello guys. I have the following question.

    We have a Markov chain with this transition matrix P : [1/3, 1/3, 1/3; 0 2/3 1/3; 1/2, 1/2, 0]

    So 1/3. 1/3, 1/3 is my first row, 0, 2/3, 1/3 the second row and 1/2, 1/2, 0 the third row.

    And I have to find the mean time to hit state 3 starting from state 1, say b(1 to 3)

    I said b(1 to 3)= 1+ 1/3*(b(1 to 3)) + 1/3* b(2 to 3)

    Now b(2 to 3) = 1+2/3 * b(2 to 3) so b(2 to 3)=3

    So I find b(1 to 3)=3

    I have a question. What I did is based on our lectures. I understand all the steps except why do we add 1 to find b(1 to 3) and b(2 to 3) i.e why not be b(1 to 3)= 1/3 * (b(3 to 3))+ 1/3*(b(1 to 3)) + 1/3* b(2 to 3) AND b(2 to 3) = 1/3 * b(3 to 3) +2/3 * b(2 to 3) so b(2 to 3)=3

    The lecturer said to us is like a forced step but for example the probability to go from 1 to 3 is 1/3 and not 1 and the probability to go from 2 to 3 is 1/3 again, not 1!

    I hope you can understand my notation!

    So can someone explain me this and also tell me if what I did is correct? Thank you very much!!!
    Last edited by Darkprince; November 7th 2011 at 12:21 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 19th 2011, 03:27 PM
  2. Replies: 3
    Last Post: December 6th 2010, 02:52 AM
  3. Replies: 1
    Last Post: September 17th 2009, 03:51 AM
  4. recurrence relations - degree of the recurrence
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 6th 2009, 07:56 PM
  5. Posting 2nd time(1st time didnt get anyhelp)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 21st 2008, 08:21 PM

Search Tags


/mathhelpforum @mathhelpforum