  The purpose of the present paper is to derive a partial differential equation
(PDE) for the single-time single-point probability density function (PDF) of
the velocity field of a turbulent flow. The PDF PDE is a highly non-linear
parabolic-transport equation, which depends on two conditional statistical
numerics of important physical significance. The PDF PDE is a general form of
the classical Reynolds mean flow equation, and is a precise formulation of the
PDF transport equation. The PDF PDE provides us with a new method for modelling
turbulence. An explicit example is constructed, though the example is seemingly
artificial, but it demonstrates the PDF method based on the new PDF PDE.
