  A general theory is presented for the photodetection statistics of coherent
radiation that has been amplified by a disordered medium. The beating of the
coherent radiation with the spontaneous emission increases the noise above the
shot-noise level. The excess noise is expressed in terms of the transmission
and reflection matrices of the medium, and evaluated using the methods of
random-matrix theory. Inter-mode scattering between $N$ propagating modes
increases the noise figure by up to a factor of $N$, as one approaches the
laser threshold. Results are contrasted with those for an absorbing medium.
