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Find the proportion of time the chain

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At all times, an urn contains 3 balls - some white balls and some black balls. At each stage, a coin having probability 0.3 of landing heads is flipped. If heads appears, then a ball is chosen at random from the urn and is replaced by a white ball; if tails appears, then a ball is chosen at random from the urn and is replaced by a black ball.

(a) Analyze this system using a Markov chain and determine its transition probability matrix.

(b) Find the proportion of time the chain spends in each state in the long run.

Reference no: EM132907287

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