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In this paper we study, using Monte Carlo simulations, the possibility todiscriminate the mass of the Ultra High Energy Cosmic Rays (UHECRs) bycombining information obtained from the maximum $X_{max}^{\mu}$ of the muonproduction rate longitudinal profile of Extensive Air Showers (EAS) and thenumber of muons, $N^{\mu}$, which hit an array of detectors located in thehorizontal plane. We investigate the sensitivity of the 2D distribution$X_{max}^{\mu}$ versus $N^{\mu}$ to the mass of the primary particle generatingthe air shower. To this purpose we analyze a set of CORSIKA showers induced byprotons and iron nuclei at energies of $10^{19}$eV and $10^{20}$eV, at fiveangles of incidence, $0^{\circ}$, $37^{\circ}$, $48^{\circ}$, $55^{\circ}$ and$60^{\circ}$. Using the simulations we obtain the 2D Probability Functions$Prob(X_{max}^{\mu},N^{\mu} \ | \ p)$ and $Prob(X_{max}^{\mu},N^{\mu} \ | \Fe)$ which give the probability that a shower induced by a proton or ironnucleus contributes to a specific point on the plane ($X_{max}^{\mu}$,$N^{\mu}$). Then we construct the probability functions $Prob(p\ | \X_{max}^{\mu},N^{\mu})$ and $Prob(Fe \ | \ X_{max}^{\mu},N^{\mu})$ which givethe probability that a certain point on the plane ($X_{max}^{\mu}$, $N^{\mu}$)corresponds to a shower initiated by a proton or an iron nucleus, respectively.Finally, a test of this procedure using a Bayesian approach, confirms animproved accuracy of the primary mass estimation in comparison with the resultsobtained using only the $X_{max}^{\mu}$ distributions.

Simulation study of the correlation ($X_{max}^{\mu}$, $N^{\mu}$) in view of obtaining information on primary mass of the UHECRs