Let $\{X_i\}_{i=1}^n$ be $n$ positive, discrete (so positive integers) and IID random variables. Let $\{c_i\}_{i=1}^n$ be constants and $$Y=\frac{\sum c_iX_i}{\big(\sum X_i\big)^2}\ \ \ ;\ \ \ Z=\frac{1}{\sum X_i}$$
I'm trying to calculate $\mathbb{E}[Y]$ and $\text{var}(Y)$ in terms of $\mathbb{E}[X_i]$'s. Similarly for expectation and variance of $Z$. I've looked at other answers related to calculating the expectation of inverses and quotients, but they deal with more general cases and involve integrals and all.
Given the assumptions about $X_i$'s that I listed out, how can $\mathbb{E}[Y]$ and $\text{var}(Y)$ be calculated?