  We present an exact model of the detection statistics of a probabilistic
source of photon pairs from which a fast, simple and precise method to measure
the source's brightness and photon channel transmissions is demonstrated. We
measure such properties for a source based on spontaneous parametric
downconversion in a periodically poled LiNbO$_3$ crystal producing pairs at 810
and 1550 nm wavelengths. We further validate the model by comparing the
predicted and measured values for the $g^{(2)}(0)$ of a heralded single photon
source over a wide range of the brightness. Our model is of particular use for
monitoring and tuning the brightness on demand as required for various quantum
communication applications. We comment on its applicability to sources
involving spectral and/or spatial filtering.
