formula

${\rm V}[X_N^{(2)}] &=& \frac{X_0^2}{N^2} {\rm V}[\sum_{i=1}^N {\cal R}_i] \\ &=& \frac{X_0^2}{N^2} \left\{ {\rm E}\left[ \left( \sum_{i=1}^N {\cal R}_i \right)^2 \right] - \left( {\rm E}\left[ \sum_{i=1}^N {\cal R}_i \right] \right)^2 \right\}$