I am currently having some problems on the following question:
Given is the function $f(x)$:
$f(x) = 0,1,2$ with probability $\frac{1}{3}$ for each.
I have to give the state space, transition probability matrix and explain why independent successive draws from $f(x)$, $X_1,X_2,\dots$, is a time-homogeneous Markov Chain.
This is really unclear to me since it seems to me that it is not a Markov Chain as the next state is independent from the previous state.
Also, would the transition matrix be a $3$ x $3$ matrix with each entry $\frac{1}{3}$?
Thank you in forward!