  (abridged) We present the first study that combines binary population
synthesis in the Galactic disk and detailed evolutionary calculations of low-
and intermediate-mass X-ray binaries (L/IMXBs). We show that the formation
probability of IMXBs with initial donor masses of 1.5--4 Msun is typically >~5
times higher than that of standard LMXBs, and suggest that the majority of the
observed systems may have descended from IMXBs. Distributions at the current
epoch of the orbital periods, donor masses, and mass accretion rates have been
computed, as have orbital-period distributions of BMPs. Several significant
discrepancies between the theoretical and observed distributions are discussed.
The orbital-period distribution of observed BMPs strongly favors cases where
the envelope of the neutron-star progenitor is more easily ejected during the
common-envelope phase. However, this leads to a >~100-fold overproduction of
the theoretical number of luminous X-ray sources relative to the total observed
number of LMXBs. X-ray irradiation of the donor star may result in a dramatic
reduction in the X-ray active lifetime of L/IMXBs, thus possibly resolving the
overproduction problem, as well as the long-standing BMP/LMXB birthrate
problem.
