  We study the Log(N)-Log(S) and X-ray luminosity function in the 2-10 keV
energy band, and the spatial (3-D) distribution of bright, log(L_X) > 34-35
erg/s, X-ray binaries in the Milky Way. In agreement with theoretical
expectations and earlier results we found significant differences between the
spatial distributions of low (LMXB) and high (HMXB) mass X-ray binaries. The
volume density of LMXB sources peaks strongly at the Galactic Bulge. HMXBs tend
to avoid the inner 3-4 kpc of the Galaxy, HMXBs are more concentrated towards
the Galactic Plane and show clear signatures of the spiral structure in their
spatial distribution. LMXB sources have a flatter Log(N)-Log(S) distribution
and luminosity function than HMXBs. The integrated 2-10 keV luminosities of
X-ray binaries, averaged over 1996--2000, are 2-3 * 10^39 (LMXB) and 2-3 *
10^38 (HMXB) erg/s. Normalised to the stellar mass and the star formation rate,
respectively, these correspond to 5 * 10^28 erg/s/M_sol for LMXBs and 5 * 10^37
erg/s/(M_sol/yr) for HMXBs. Due to the shallow slopes of the luminosity
functions the integrated emission of X-ray binaries is dominated by the 5-10
most luminous sources which determine the appearance of the Milky Way in the
standard X-ray band for an outside observer. In particular variability of
individual sources or an outburst of a bright transient source can increase the
integrated luminosity of the Milky Way by as much as a factor of ~2. Although
the average LMXB luminosity function shows a break near the Eddington
luminosity for a 1.4 M_sol neutron star, at least 11 sources showed episodes of
super-Eddington luminosity during ASM observations. We provide the maps of
distribution of X-ray binaries in the Milky Way in various projections, which
can be compared to images of nearby galaxies taken by CHANDRA and XMM-Newton.
