Come up a random system which is not a Markov ChainWe are le

Come up a random system which is not a Markov Chain.(We are learning Applied Linear Algebra)

Solution

Let a basket contains two yellow balls and one green ball. One ball was drawn yesterday, one ball was drawn today, and the final ball will be drawn tomorrow. All of the draws are \"without replacement\".

1) Suppose you know that today\'s ball was yellow, but you have no information about yesterday\'s ball. The chance that tomorrow\'s ball will be yellow is 1/2. That\'s because the only two remaining outcomes for this random experiment are \"y,y,g\" and \"g,y,y\".

2) On the other hand, if you know that both today and yesterday\'s balls were yellow, then you are guaranteed to get a green ball tomorrow.

This discrepancy shows that the probability distribution for tomorrow\'s color depends not only on the present value, but is also affected by information about the past. This stochastic process of observed colors doesn\'t have the Markov property.

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