  We calculate the contribution to the cosmic x-ray background (CXB) of a
population of power law spectrum sources with spectral indices distributed over
a broad range of values. The composite spectrum of this source population is
significantly harder than that given by the power law having the average value
of spectral indices. Starting from spectral distributions which are
approximately those observed from quasars, it is possible to reproduce the CXB
spectrum from ~0.5 keV to ~20 keV. If the spectra of quasars steepen at around
100 keV, the resulting composite spectrum nearly perfectly fits the CXB in the
even broader energy range, up to ~100 keV. The QSO population with broadly
distributed spectral parameters is also characterized by a significant
discrepancy between the results of hard and soft x-ray source counts. The same
population of sources yields about three times more sources at 10 keV than at
the corresponding flux at 1 keV, similarly to what is found from the comparison
of HEAO A-1/Ginga and Einstein/ROSAT measurements. Thus, by allowing the
spectra of QSO's to span a broad range of spectral indices, it is possible to
reproduce both the CXB spectrum and account for the apparent differences in
number counts in different energy bands.
