A fair die is thrown repeatedly. Let be the sum of the outcomes, and let be the remindeer when is divided by 4(that is is the sum of the first n throws reduced modulo 4).

a) Show that 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 to see what is going on in this chain as I find it difficult to understand the question.

thanks for any help.