  Thanks to the Gaia archived data, we find a correlation between the stellar
types (with different average mass) and the scale parameters of the
Maxwell-Boltzmann (MB) distribution of their dispersion velocities, by
averaging over their age range. As expected, the late-type stars and brown
dwarfs have wider velocity (MB) distributions with larger scale parameters than
early-type ones. According to this correlation, we conclude that the dispersion
velocities of brown dwarfs should have an MB profile with the scale parameter
$a\simeq 111.9~\rm{km/s}$. This mass-velocity dispersion relation confirms the
known age-velocity relation and additionally reveals the dependence of the
stellar dispersion velocity to mass in the given average age. By considering
this correlation as well as a brown dwarf population, we simulate microlensing
events detectable by MOA-II toward the Galactic bulge fields gb5 and gb9 which
were intensively observed during that observation. From this simulation, the
average values of the events' duration are $18.72$ and $18.68~$days, which are
close to the observational amounts, i.e., $17.4$ and $22.2~$days. In the
simulation, we do not consider any extra free-floating exoplanet population. A
population of speedy brown dwarfs with the corrected dispersion velocity
profile generates the observational results of MOA-II and there is no need to
include free-floating exoplanets.
