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.
Bob
Problem:
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?
Answer:
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.