  A scheme for analyzing Thomson scattering of x-rays by warm dense matter,
based on the average-atom model, is developed. Emphasis is given to x-ray
scattering by bound electrons. Contributions to the scattered x-ray spectrum
from elastic scattering by electrons moving with the ions and from inelastic
scattering by free and bound electrons are evaluated using parameters (chemical
potential, average ionic charge, free electron density, bound and continuum
wave functions, and occupation numbers) taken from the average-atom model. The
resulting scheme provides a relatively simple diagnostic for use in connection
with x-ray scattering measurements. Applications are given to dense hydrogen,
beryllium, aluminum, titanium, and tin plasmas. At high momentum transfer,
contributions from inelastic scattering by bound electrons are dominant
features of the scattered x-ray spectrum for aluminum, titanium, and tin.
