Determine its transition probability matrix

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Reference no: EM132169251

Three white and three black balls are distributed in two urns in such a way that each contains three balls. We will say that the system is in state i, i = 0, 1, 2, 3, if the first urn contains i, white balls. At each step, we draw one ball from each urn – the ball drawn from the first urn is placed into the second, and the ball from the second urn is placed into the first. Let Xn denote the state of the system after the nth step.

Explain why {Xn, n = 0, 1, 2, …} is a Markov chain.

Draw the state transition diagram.

Determine its transition probability matrix.

What are the communicating classes? Why?

Is the Markov chain irreducible? Why?

What is the period of each state? Why?

Which states are transient? Which are recurrent? Why?

Reference no: EM132169251

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