Results 1 to 8 of 8

Math Help - Markov chain problem

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    5

    Markov chain problem

    The coat of a certain breed of cat can be either black, white or grey.
    When a black-coated male is crossed with a white-coated female, the offspring kitten has a 50% chance of having a black coat, and a 50% chance of having a white coat.

    When a white-coated male is crossed with a white-coated female, the offspring kitten has a 20% chance of having a black coat, a 60% chance of having a white coat and a 20% chance of haing a grey coat.

    When a grey-coated male is crossed with a white-coated female, the offspring kitten has a 10% chance of having a black coat, a 45% chance of having a white coat and a 45% chance of having a grey coat.

    (a) Assume that each successive generation of cats is produced by crossing all cats with a white-coated female. Write down the transition matrix for this Markov process.

    (b) If initially there are equal numbers of black-coated and white-coated cats, and no grey-coated cats, what percentage of the next generation will be grey-coated?

    (c) In the long run, what percentage of cats will have black, white and grey coats?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2009
    Posts
    20

    I hope this helps

    I need to rethink my response!
    Last edited by symmetry7; October 18th 2009 at 04:54 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    5
    there should be a vector that multipies with the transition matrix
    P . x1 = x2
    but i wasn't sure what that vector should be.
    if in the case of your matrix,
    i assume the vector equation in question (b) is
    0.5 ? as there are equal numbers of black and white cats ? correct me if i am wrong
    0.5
    0
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2009
    Posts
    20

    idea

    the vector should be a 3x1 to be able to multiply with the 3x3 matrix ...
    so maybe (0.5 0.6 0.45)?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2009
    Posts
    20

    however

    The matrix i originally posted

    0.5 0.5 0
    0.2 0.6 0.2
    0.1 0.45 0.45

    is defined in the question as being a result of each colour interbreeding with white coats ... hmmm a little confusing
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2009
    Posts
    5
    im sure you got the transition matrix right, but i dont understand why
    ...............(0.5 0.5 0 )
    (0.5 0.5 0)(0.2 0.6 0.2)
    ..............(0.1 0.45 0.45)
    links to the next generation of grey cats
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2009
    Posts
    20

    how about this?

    If you multiply that vector with your matrix you'll get a vector (0.5 0.4 0.275) ... hmmm
    Last edited by symmetry7; October 18th 2009 at 06:26 AM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    May 2009
    Posts
    20

    part c

    Either way .. I'm not too sure about b, but, Long term transition probabilities I'm fairly sure simply involve taking your matrix P to a high power... I think you'll find that for B, W, and G respectively you'll get something like 25.7% for B, 54.45% for W, and 19.8 % for G

    There's a bit of error in these percentages because all should add up to exactly 1 due to the stochastic nature of the matrix P
    Last edited by symmetry7; October 18th 2009 at 06:28 AM.
    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 problem
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: May 23rd 2011, 01:55 PM
  3. Markov Chain problem.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 18th 2011, 04:40 AM
  4. Markov Chain Problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 1st 2009, 08:29 PM
  5. Replies: 2
    Last Post: October 28th 2008, 07:32 PM

Search Tags


/mathhelpforum @mathhelpforum