  The X-ray luminosity functions of galaxies have become a useful tool for
population studies of X-ray binaries in them. The availability of long term
light-curves of X-ray binaries with the All Sky X-ray Monitors opens up the
possibility of constructing X-ray luminosity functions, by also including the
intensity variation effects of the galactic X-ray binaries. We have constructed
multiple realizations of the X-ray luminosity functions (XLFs) of Milky Way,
using the long term light-curves of sources obtained in the 2-10 keV energy
band with the RXTE-ASM. The observed spread seen in the value of slope of both
HMXB and LMXB XLFs are due to inclusion of variable luminosities of X-ray
binaries in construction of these XLFs as well as finite sample effects. XLFs
constructed for galactic HMXBs in the luminosity range 10^{36} - 10^{39}
erg/sec is described by a power-law model with a mean power-law index of -0.48
and a spread due to variability of HMXBs as 0.19. XLFs constructed for galactic
LMXBs in the luminosity range 10^{36} - 10^{39} erg/sec has a shape of cut-off
power-law with mean power-law index of -0.31 and a spread due to variability of
LMXBs as 0.07.
