Probabilistic distributions of $M/L$ values for ultra-faint dwarf
  spheroidal galaxies: stochastic samplings of the IMF
  As the total mass of stellar populations of fixed IMF, age and metallicity
tends to infinity, resulting intrinsic $M/L$ values quickly converge to fixed
numbers associated to the particulars of the stars in question. When going to
very small stellar populations, the stochastic sampling of the IMF will yield
an inherent spread for the $M/L$ values, which will become probabilistic
quantities. For the recently discovered ultra-faint dwarf spheroidal galaxies,
with total luminosities dropping below 10^3 L_V/L_o, it is important to asses
the amplitude of the probabilistic spread in inherent $M/L$ values. The total
baryonic masses of these systems are usually estimated from their luminosities,
assuming fixed, deterministic $M/L$ values, suitable for the infinite
population limit. These total baryonic masses are crucial for the testing of
structure formation scenarios, as the local ultra-faint dwarf spheroidals
represent the most extreme galactic scales known. Also subject to reliable
$M/L$ values, is the use of these systems as possible discriminants between
dark matter and modified gravity theories. By simulating large collections of
stellar populations, each consisting of a particular collection of individual
stars, we compute statistical distributions for the resulting $M/L$ values. For
total numbers of stars in the range of what is observed for the ultra-faint
dwarf spheroidals, inherent $M/L$ values of stellar populations can be expected
to vary by factors of upwards of 3, interestingly, systematically skewed
towards higher values than what corresponds to the infinite population limit.
This can explain part of the spread in reported baryonic masses for these
systems, which also appear as shifted systematically towards high dark to
baryonic mass ratios at fixed stellar velocity dispersions.
