This paper presents a new approach to solve the Fokker-Planck-Kolmogorov Equation (FPKE). The main purpose of this research is to provide a method-ology to efficiently determine the time-varying state probability density function (PDF) for a general nonlinear system. Collocation-based methods often rely on high order cubature points, and require a large number of basis functions to accurately determine the solution of a partial differential equation. The recently developed Conjugate Unscented Transform is there-fore proposed to provide a minimal set of collocation points. In conjunction with this minimal cubature point method, by employing an l1 norm minimization to optimally select the appropriate basis functions from the larger complete dictionary of polynomial basis functions, a minimal polynomial expression for the state PDF is obtained at each time step.