A new path integral representation of the quantum density of states (DOS) and distribution functions of strongly correlated fermions are derived in the Wigner formulation of quantum mechanics. A new path integral Monte Carlo approach to calculate DOS and thermodynamic functions is suggested. Using 3 He as an interesting example, we calculate the DOS, internal energy distribution (IED), momentum distribution functions (MDFs), spin-resolved radial distribution functions at different densities and temperatures. The physical meaning and parameters of exchange-correlation holes, the quantum oscillations of IEDs and DOS as well as the high-momentum asymptotics (‘quantum tails’) of MDFs have been considered and explained.