\mathrm{E}\left[\frac{1}{\left(1+X\right)\left(1+Y\right)\left(1+Z\right)}\right] = \mathrm{E}\left(\frac{1}{1+X} \cdot \frac{1}{1+Y} \cdot \frac{1}{1+Z}\right) = \mathrm{E}\left(\frac{1}{1+X}\right) \cdot \mathrm{E}\left(\frac{1}{1+Y}\right) \cdot \mathrm{E}\left(\frac{1}{1+Z}\right) =