Let $Z_0,Z_1,Z_2,...$ be i.i.d. random variables,taking values $+1$ and $-1$ each with probability $1/2$. Let $S_n=\sum_{i=0}^n Z_i$(where we take $S_0=0$).Let $X_n=\sum_{j=0}^n S_j$. say whether or not $X_n$ is a time-homogeneous Markov chain? If yes, give the transitional matrix or the transitional diagram. If no, prove it.
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What have you tried yourself? – abacaba May 15 '22 at 16:24
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I tried to write x in terms of z, but it didn't work. – Aya May 15 '22 at 17:56