Gain variance

If there is a variance $\sigma_{\mu}^{2}$ in the gain $\mu$ itself, this will also contribute to the variance in the number of output electrons. If this variance is much smaller than the $\left (\mu -1 \right )^{2}$ (and also smaller than $\left (2 - \mu \right )^{2}$ for model 2) as seems likely for a real electronic device, the contribution this makes to the output variance from an individual gain stage is negligible for both of the models when combined with the statistical noise described above.