is it a Markov Chain

Question

Example:

"When rolling regular fair six-sided die repeatedly, the number shown."

The answer I was given was, yes, it is a a Markov Chain.But according to my understanding, a Markov Chain is something like you only need to know the current state to predict the future stat. In this rolling dice example, even the current state cannot be used to predict the future state?

Answer 1

It's still a markov chain. All you need for a markov chain is the condition that

$$P(X_i=v_i| X_{1} =v_1\land X_2=v_2\land\cdots\land X_{i-1}=v_{i-1} = P(X_i=v_i|X_{i-1}=v_{i-1}) $$

and this condition is clearly satisfied here (since both sides of the equation are equal to $\frac16$).

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Intuitively, a Markov chain is

any sequence of events where, given one state, you can calculate the probabilities of the next state.

Note that this is not the same as

any sequence of events where you can calculate the probabilities of the next state from the current state.