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 Post subject: Markov chain - steady state solutionPosted: Tue, 17 Jul 2012 16:20:17 UTC
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Joined: Tue, 17 Jul 2012 15:46:12 UTC
Posts: 1
Hi at all!
I have this exercise:

Consider a system with two component. We observe the state of system every hour. A given
component operating at time n has:
(a) probability p of falling before the next observation time n+1.
(b) probability r of begin repaired by time n+1, independent of how long the component has
been in failed state.
The component failures and repairs are mutually independent events.
Let Xn the number of components in operation at time n. Then X = {Xn |0, 1, ...} is a discrete-time
homogeneous Markov chain with state space {0, 1, 2}.
Does the steady-state occupancy vector exist for this chain? Show why and why not. Obtain
the steady-state probability vector if it exists.

Ok i have already compute the probability transition matrix.
And i know that the chain admit steady-state probability vector, and i computed it solving linear system
but what is steady-state occupancy vector?

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