Below is a problem that I did. I got the answer in the book, but I am not confident that I got it right. I am hoping that somebody here can verify that my solution is correct.

Consider a random process $X(n) = \{ X_n, \, n \leq 1\}$, where \begin{eqnarray*} X_n &=& Z_z + Z_2 + ... Z_n \\ \end{eqnarray*} and $Z_n$ are iid r.v.'s with zero mean and variance $\sigma^2$. Is X(n) stationary?
For $X(n)$ to be a stationary distribution we would need $Z_1$ and $Z_1 + Z_2$ to have the same distribution. While they have the same mean, they do not have the same variance. Therefore, this random process is not stationary.

  • 1
    $\begingroup$ Your reasoning is correct. $\endgroup$ – Math1000 Oct 16 '17 at 6:22

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