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For words problems, I'm having trouble defining what state should be in a Markov chain, when the states aren't that obvious. Are there any general procedures that should be followed in order to identify what a state should be?

An example I'm having trouble with would be something like this where to me the states aren't obvious.

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Jonathan Wang
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1 Answers1

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Here the states of the markov chain are the types of exams (so there are three states). You can tell cause each time we transfer to a new exam according to some probability rule depending on the exam we just had.

spaceisdarkgreen
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  • Okay, so if the states are the exams, then should the transition probabilities be whether the class does well or whether the class does badly since there are different scenarios? – Jonathan Wang Jan 28 '18 at 00:08
  • The transition probabilities are the probability next exam will be type $i$ if the current exam is type $j.$ These can be computed from the probability of doing well combined with the probability of the next exam given that they did well/poorly. – spaceisdarkgreen Jan 28 '18 at 00:17
  • Is there a general guideline on how to determine what states should be considered as for some arbitrary question? – Jonathan Wang Jan 28 '18 at 01:57