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**charikaar** A fair die is thrown repeatedly. Let $\displaystyle S_{n}$ be the sum of the outcomes, and let $\displaystyle R_{n}$ be the remindeer when $\displaystyle S_{n}$ is divided by 4(that is $\displaystyle R_{n}$ is the sum of the first n throws reduced modulo 4).

a) Show that $\displaystyle R_{n}$ ia a Markov chain on state space {0,1,2,3}.

b) what are the transitoin probabilities for this chain?

Can you please give me numerical example of $\displaystyle R_{n}$ to see what is going on in this chain as I find it difficult to understand the question.

thanks for any help.