  In 1945, Dirac attempted to develop a "formal probability" distribution to
describe quantum operators in terms of two non-commuting variables, such as
position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting
quasi-probability distribution is a complete representation of the quantum
state and can be observed directly in experiments. We measure Dirac's
distribution for the quantum state of the transverse degree of freedom of a
photon by weakly measuring transverse x so as to not randomize the subsequent p
measurement. Further, we show that the distribution has the classical-like
feature that it transforms (e.g., propagates) according to Bayes' law.
