formula

${\rm V}[X_N^{(2)}] &=& \frac{X_0^2}{N^2} \left\{ 2\sum_{j>i}\mu^{j-i}(\mu^2 +\sigma^2)^{N-j+1} + \sum_{i=1}^N (\mu^2 +\sigma^2)^i - \left( \sum_{i=1}^{N}\mu^i \right)^2 \right\} \\ &\equiv& \frac{X_0^2}{N^2} \left\{ 2\sum_{j>i}\mu^{j-i}\nu^{N-j+1} + \sum_{i=1}^N \nu^i - \left( \sum_{i=1}^{N}\mu^i \right)^2 \right\}$