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Markov Chains and absorption probabilites

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Could someone please help me with this question?

    A single-celled organism contains N particles, some of which are of type A, the others of
    type B . The cell is said to be in state i , where 0<=i<=N if it contains exactly i particles
    of type A. Daughter cells are formed by cell division, but fi rst each particle replicates itself;
    the daughter cell inherits N particles chosen at random from the 2i particles of type A
    and 2N-2i of type B in the parent cell.

    Find the absorption probabilities and expected times to absorption for the case N = 3.


    2. Relevant equations



    3. The attempt at a solution
    So far i have that the absorbing states are i=0 and i=3 but cant work out the probabilities or times to absorption. Don't know where to start now that i have my absorbing states
     
  2. jcsd
  3. Feb 4, 2013 #2

    Ray Vickson

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    From state i, the (A,B) numbers of the daughter are determined by N independent "draws", with probabilities P(A) = i/N and P(B) = 1-P(A) in each draw.
     
  4. Feb 4, 2013 #3
    So is the probability of say reaching state 1 from state 2 1/5 from the number of possible combinations of the daughter cell or am i going about this the wrong way?
     
  5. Feb 4, 2013 #4

    Ray Vickson

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    I have said all I intend to say on the subject.
     
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