# A Two-State, Discrete-Time Markov Chain

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Consider a system that is always in one of two states, 1 or 2. Every time a clock ticks, the system updates itself according to a 2×2 matrix of transition probabilities, the entry of which gives the probability that the system moves from state to state at any clock tick. A twoÃƒÂ¢Ã‚Â€Ã‚Âstate Markov chain is a system like this, in which the next state depends only on the current state and not on previous states. Powers of the transition matrix approach a matrix with constant columns as the power increases. The number to which entries in the column converge is the asymptotic fraction of time the system spends in state .

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Contributed by: Chris Boucher (March 2011)

Open content licensed under CC BY-NC-SA

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"A Two-State, Discrete-Time Markov Chain"

http://demonstrations.wolfram.com/ATwoStateDiscreteTimeMarkovChain/

Wolfram Demonstrations Project

Published: March 7 2011