  We study the possibility of primary mass estimation for Ultra High Energy
Cosmic Rays (UHECR's) using the $X_{max}^{\mu}$ (the height where the number of
muons produced on the core of Extensive Air Showers (EAS) is maximum) and the
number $N^{\mu}$ of muons detected on ground. We use the 2D distribution -
$X_{max}^{\mu}$ against $N^{\mu}$ in order to find its sensitivity to the mass
of the primary particle. For that, we construct a 2D Probability Function
$Prob(p,Fe \ | \ X_{max}^{\mu},N^{\mu})$ which estimates the probability that a
certain point from the plane $(X_{max}^{\mu}$, $N^{\mu})$ corresponds to a
shower induced by a proton, respectively an iron nucleus. To test the
procedure, we analyze a set of simulated EAS induced by protons and iron nuclei
at energies of $10^{19} eV$ and $20^{\circ}$ zenith angle with CORSIKA. Using
the Bayesian approach and taking into account the geometry of the infill
detectors from the Pierre Auger Observatory, we observe an improvement in the
accuracy of the primary mass reconstruction in comparison with the results
obtained using only the $X_{max}^{\mu}$ distributions.
