Please help with this question, I have no clue where to even start. Please please please help!!
2026-03-30 10:11:08.1774865468
Markov Chain, Irreducible, Stationary distribution
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It's fairly easy to convince yourself that $X_{n+1}$ only depends on $X_n$, not on all previous states, which makes this a Markov chain. For a formal proof you will need the recurrence $X_{n+1} = X_n + Y_{n+1} \pmod{10}$, as well as independence of $X_n$ and $Y_{n+1}$.
State space are all possible values $X_n$ can take, but $X_n$ is some integer modulo $10$. What are its possible values?
Transition probabilities. Think about $Y_{n+1}$ has to be to map particular values of $X_n$ to values in $X_{n+1}$ using the above-mentioned recurrence.
Finding the stationary distribution would involve solving $x = xP$...