I am thinking of finding $P(X_3=r|X_0=s)$ i.e $P_{s,r}^3$. But with the given data i am unable to go ahead. Am I thinking correctly? How to solve this problem?
2026-04-07 11:14:10.1775560450
Distribution of $X_n$ Stochastic process
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Let's call the initial distribution $\mu$ , i.e. $\mu = (0.5, 0.5, 0)$. In your lecture notes you should have a formula like this $$ P_\mu(X_n = x) = P^n \mu$$ (maybe read up on that a bit) hence you should do something like $P^2 * \mu$. I hope you can figure out why the exponent is two here, rather than three.