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February 4th, 2013, 02:18 PM   #1
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Markov Chains and absorption probabilites

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 first 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.

I have that the absorbing states are i=0 and i=3 but need help finding the transition matrix P, could anyone work out the transition probabilities when starting in state i=1 and state i=2 and explain how i am to find them please
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