  We illustrate the use of the statistical method of moments for determining
the position and momentum distributions of a quantum object from the statistics
of a single measurement. The method is used for three different, though
related, models; the sequential measurement model, the Arthurs-Kelly model and
the eight-port homodyne detection model. In each case, the method of moments
gives the position and momentum distribution for a large class of initial
states, the relevant condition being the exponential boundedness of the
distributions.
