Vibration of a non-linear system under random parametric excitations was evaluated by probabilistic methods. The non-linear characteristic terms of a system were quasi-linearized and excitation terms remained as they were. An analytical method where the square mean of error was minimized was used. An alternative method was an energy method where the damping energy and restoring energy of the linearized system were equalized to those of the original nonlinear system. The numerical results were compared with those obtained by Monte Carlo simulation. A new method was proposed from the comparison of those results. Finally the results obtained by the combined method showed good agreement with those obtained by Monte Carlo simulation.