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The main question we want to answer is: “As a Markov chain keeps running, what kind of behavior does each state have?”
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This is quite a hard question to answer straight away, so perhaps we should start with a different question.
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Introduction One of those things that is easy to understand conceptually but hard to grasp once we look at the math is doing multi-step transition probabilities.
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In my last post, I covered the gambler's ruin, where a gambler was trying to win some money on roulette so he could pay child support to his ex-wife.
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You are entering a casino to win some money to pay your ex-wife's child support.
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Imagine you and your friend are standing on the sidewalk and you suggest a fun game.
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Outside my apartment the sidewalks are paved with stone slabs.
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When Russian mathematician Pavel Nekrasov looked at "moral statistics," with its yearly rates of crimes, suicides, and marriages, he noticed something unsettling: the data was flat.