  In relativistic heavy-ion collisions, event-by-event fluctuations are known
to have non-trivial implications. Even though the probability distribution is
geometrically isotropic for the initial conditions, the anisotropic
$\varepsilon_n$ still differs from zero owing to the statistical fluctuations
in the energy profile. On the other hand, the flow harmonics extracted from the
hadron spectrum using the multi-particle correlators are inevitably subjected
to non-vanishing variance due to the finite number of hadrons emitted in
individual events. As one aims to extract information on the fluctuations in
the initial conditions via flow harmonics and their fluctuations, finite
multiplicity may play a role in interfering with such an effort. In this study,
we explore the properties and impacts of such fluctuations in the initial and
final states, which both notably appear to be statistical ones originating from
the finite number of quanta of the underlying system. We elaborate on the
properties of the initial-state eccentricities for the smooth and
event-by-event fluctuating initial conditions and their distinct impacts on the
resulting flow harmonics. Numerical simulations are performed. The possible
implications of the present study are also addressed.
