Path integral Monte Carlo and density functional techniques are used to study a two-electron system for which exact results can be obtained. The energy and single-particle density are calculated for the lowest singlet and triplet states. The results show that both methods give reasonable agreement with the exact answer. The path integral calculations also give the correlated two-electron wave functions, which compare favorable with the exact results. Finally, the exchange-correlation hole is evaluated from the path integral simulations. The study demonstrates that path integral calculations are as accurate as density functional calculations and yield additional information in the form of the correlated density matrix.