  We discuss the energy distribution of free-electron Fermi-gas, a problem with
a textbook solution of Gaussian energy fluctuations in the limit of a large
system. We find that for a small system, characterized solely by its heat
capacity $C$, the distribution can be solved analytically, and it is both
skewed and it vanishes at low energies, exhibiting a sharp drop to zero at the
energy corresponding to the filled Fermi sea. The results are relevant from the
experimental point of view, since the predicted non-Gaussian effects become
pronounced when $C/k_B \lesssim 10^3$ ($k_B$ is the Boltzmann constant), a
regime that can be easily achieved for instance in mesoscopic metallic
conductors at sub-kelvin temperatures.
