  Relativistic dissipative fluid dynamics is a common tool to describe the
space-time evolution of the strongly interacting matter created in
ultrarelativistic heavy-ion collisions. For a proper comparison to experimental
data, fluid-dynamical calculations have to be performed on an event-by-event
basis. Therefore, fluid dynamics should be able to reproduce, not only the
event-averaged momentum anisotropies, $<v_{n}>$, but also their distributions.
In this paper, we investigate the event-by-event distributions of the
initial-state and momentum anisotropies $\epsilon_n$ and $v_n$, and their
correlations. We demonstrate that the event-by-event distributions of relative
$v_n$ fluctuations are almost equal to the event-by-event distributions of
corresponding $\epsilon_n$ fluctuations, allowing experimental determination of
the relative anisotropy fluctuations of the initial state. Furthermore, the
correlation $c(v_2,v_4)$ turns out to be sensitive to the viscosity of the
fluid providing an additional constraint to the properties of the strongly
interacting matter.
