In this study, we simulated a statistical model of FCS(fluorescence correlation spectroscopy) based on a Poisson process to understand and explain observations of the experiment performed on molecules of ultra-low concentration by the home-built laser-scanning confocal microscope. The statistical model confirmed that the relative mean square amplitude of fluctuations is shown to be inversely proportional to the average number of molecules, even in the ultra-low concentration, if some conditions are satisfied. Signal-to-noise ratio and the variability of dwelling time under the confocal volume were found to be effective conditions for the experiment.