Results 1 to 8 of 8

Math Help - Markov chain

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    12

    Markov chain

    hi


    if someone could maybe give me an idea as to how to answer this question please.

    I have attached a file with my workings since the formatting is a lot clearer to read.



    How do i put all this into a matrix?, i mean i have 10 probabilities only the hint suggests the matrix is 6*6??



    help appreciated..
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by 1cookie View Post
    hi


    if someone could maybe give me an idea as to how to answer this question please.

    I have attached a file with my workings since the formatting is a lot clearer to read.



    How do i put all this into a matrix?, i mean i have 10 probabilities only the hint suggests the matrix is 6*6??



    help appreciated..
    List the possible states at a generation and lable them,

    Thus we could take state:

    1: aa,aa
    2: aa,ab
    3: aa,bb
    4: ab,ab
    5: ab,bb
    6: bb,bb

    Thus our state vector x is six dimensional with the probability of the state
    i being x_i.

    Now we need to compile the transition matrix A, where A_{i,j} is the probability
    of ending in state i when we start in state j.

    An absorbing state is one which once you get into it you cannot leave it, so
    from what we know about the model we know that state 1:aa,aa and state
    6: bb, bb are absorbing, and the associated element of A corresponding to
    the transitions from 1 to 1 is 1, and from 6 to 6 is also 1.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    12
    Quote Originally Posted by CaptainBlack View Post
    List the possible states at a generation and lable them,

    Thus we could take state:

    1: aa,aa
    2: aa,ab
    3: aa,bb
    4: ab,ab
    5: ab,bb
    6: bb,bb

    Thus our state vector x is six dimensional with the probability of the state
    i being x_i.

    Now we need to compile the transition matrix A, where A_{i,j} is the probability
    of ending in state i when we start in state j.

    An absorbing state is one which once you get into it you cannot leave it, so
    from what we know about the model we know that state 1:aa,aa and state
    6: bb, bb are absorbing, and the associated element of A corresponding to
    the transitions from 1 to 1 is 1, and from 6 to 6 is also 1.

    RonL
    hi Captain Black

    do i multiply the probabilities?? e.g. ab,ab = 1/3*1/3*1/3=1/27 ??
    Last edited by 1cookie; March 15th 2008 at 11:22 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by 1cookie View Post
    hi Captain Black

    do i multiply the probabilities?? e.g. ab,ab = 1/3*1/3*1/3=1/27 ??
    Your diagrams provide all you need to compute the probabilities.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2007
    Posts
    12
    Quote Originally Posted by CaptainBlack View Post
    Your diagrams provide all you need to compute the probabilities.

    RonL
    im looking at the parents....do i need to be looking at the offspring to construct the matrix??
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by 1cookie View Post
    im looking at the parents....do i need to be looking at the offspring to construct the matrix??
    To construct the matrix you need to look at the transition probabilities from each parent state to offspring state.

    RonL
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2007
    Posts
    12
    Quote Originally Posted by CaptainBlack View Post
    To construct the matrix you need to look at the transition probabilities from each parent state to offspring state.

    RonL
    im trying that, only it's confusing the hell out of me..:-), i mean for a matrix..


    ab bb aa

    aa


    ab


    bb


    im not a statistical person but...all parents.... and the probs just dont fit....




    ab bb aa is supposed to represent the top row
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Oct 2007
    Posts
    12
    Quote Originally Posted by CaptainBlack View Post
    To construct the matrix you need to look at the transition probabilities from each parent state to offspring state.

    RonL


    well they all sum to 6, do i scale them down to sum(p: x,y,z)=1??



    i just dont get it!!




    ditto

    now we need a transition matrix A, where A_i,j is the probability of ending in state i given we start in state j.


    from 4: ab,ab, possibilities for offspring are: aa,bb or ab and we have to repeat the process for all offspring. This gives us


    1. aa,bb,ab
    2. bb,aa,ab
    3. ab,aa,bb
    4. ab,bb,aa
    5. aa,ab,bb
    6. bb,ab,aa


    the above possibilities.


    am i right to say that the selected offspring being also ab,ab, is (1/2*1/2*1/2)+(1/2*1/2*1/2)+...+(1/2*1/2*1/2) six times, or 6(1/8)??

    And will my matrix need to be a 6*6 with aa,aa,ab,ab,bb,aa for rows and aa,ab,ab,bb,bb,bb for cols (in any order)??
    thanks


    help appreciated..
    Last edited by 1cookie; March 16th 2008 at 05:58 AM. Reason: a bit obnoxious!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Markov Chain of random variables from a primitive markov chain
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 19th 2011, 09:12 AM
  2. Markov Chain Help
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: June 28th 2010, 08:37 AM
  3. Markov Chain
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: December 12th 2009, 05:52 PM
  4. Markov Chain HELP!!!!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 9th 2009, 10:28 PM
  5. Replies: 2
    Last Post: October 28th 2008, 07:32 PM

Search Tags


/mathhelpforum @mathhelpforum