If you have a k-th order Markov chain on a state space of cardinality m, explain...

 

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If you have a k-th order Markov chain on a state space of cardinality m, explain how you can always represent it as a first-order Markov chain on a larger state space and find the cardinality if this enlarged state space. If you have a k-th order Markov chain on a state space of cardinality m, explain how you can always represent it as a first-order Markov chain on a larger state space and find the cardinality if this enlarged state space.

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