  As the era of high precision cosmology approaches, the empirically determined
power spectrum of the microwave background anisotropy, $C_l$, will provide a
crucial test for cosmological theories. We present a unified semi-analytic
framework for the study of the statistical properties of the $C_l$ coefficients
computed from the results of balloon, ground based, and satellite experiments.
An illustrative application shows that commonly used approximations {\it bias}
the estimation of the baryon parameter $\Omega_b$ at the 1% level even for a
satellite capturing as much as $\sim 70$% of the sky.
