Let $\{X(t), t\ge 0\}$ and $\{Y(t),t\ge 0\}$ be independent Poisson processes with parameters $\lambda_1$ and $\lambda_2$, respectively. Define $Z_1(t)=X(t)+Y(t)$, $Z_2(t)=X(t)-Y(t)$, $Z_3(t)=X(t)+k$, $k$ a positive integer. Determine which of the above processes are Poisson and find $\lambda$.
Any help is appreciated! This is not homework! Thanks.