This paper presents equations and computational graphs that determine the optimally tuned and damped dynamic vibration absorber attached to a linear system subjected to stationary random excitation. The optimization criterion is to minimize a performance measure defined by the mean square acceleration response of the primary system to unit input acceleration (assumed to be ideal white noise). The optimum design conditions of dynamic absorber can be formulated if the primary system has no damping. If there is damping in the primary system, the optimum conditions are obtained from the numerical solution of simultaneous equations. The optimum conditions obtained here are different from the classical ones evaluated by the so-called Ormondroyd-Den Hartog theory. It is due to the difference in the performance measure in these theories. The optimum conditions are tested on a vibratory model. It can be shown that a properly designed dynamic absorber operates efficiently for reducing the vibration induced by random excitation.