0
Let $Z = \sum_{r=1}^{\infty}rX_{r}$, where $X_{r}$ is of Poisson distribution with intensity rate $\displaystyle \frac{1}{r^{2}}$, $r \geq 1$. I need to prove that $Z$ is finite with probability $1$.
First off, I am not sure if this problem is asking me to 1) Prove that $Z$ is finite AND has pro...
