  We discuss a specific model of elliptic flow fluctuations due to Gaussian
fluctuations in the initial spatial $x$ and $y$ eccentricity components
$\left\{\mean{(\sigma_y^2-\sigma_x^2)/(\sigma_x^2+\sigma_y^2)},
\mean{2\sigma_{xy}/(\sigma_x^2+\sigma_y^2)} \right\}$. We find that in this
model $\vfour$, elliptic flow determined from 4-particle cumulants, exactly
equals the average flow value in the reaction plane coordinate system,
$\mean{v_{RP}}$, the relation which, in an approximate form, was found earlier
by Bhalerao and Ollitrault in a more general analysis, but under the same
assumption that $v_2$ is proportional to the initial system eccentricity. We
further show that in the Gaussian model all higher order cumulants are equal to
$\vfour$. Analysis of the distribution in the magnitude of the flow vector, the
$Q-$distribution, reveals that it is totally defined by two parameters,
$\vtwo$, the flow from 2-particle cumulants, and $\vfour$, thus providing
equivalent information compared to the method of cumulants. The flow obtained
from the $Q-$distribution is again $\vfour=\mean{v_{RP}}$.
