Consider a point process $\Phi=(X_i)$ defined on $[0,1]$.
Is there any formula for computing $$ \mathbb{E}\left[\frac{\sum_{X_i\in \Phi}X_i^d}{(\sum_{X_i\in \Phi}X_i)^d}\right]? $$
Campbell’s theorem (formula) seems to be related but not actually what I want. Any references/suggestions?