  Efforts are being made to observe the 21-cm signal from the 'cosmic dawn'
using sky-averaged observations with individual radio dipoles. In this paper,
we develop a model of the observations accounting for the 21-cm signal,
foregrounds, and several major instrumental effects. Given this model, we apply
Markov Chain Monte Carlo techniques to demonstrate the ability of these
instruments to separate the 21-cm signal from foregrounds and quantify their
ability to constrain properties of the first galaxies. For concreteness, we
investigate observations between 40 and 120 MHz with the proposed DARE mission
in lunar orbit, showing its potential for science return.
