An optimal single DOF dynamic absorber is presented. A tremor has a random nature and then the system is subjected to a random excitation instead of a sinusoidal one; so the $H_2$ optimization criterion is probably more desirable than the popular $H_{infty}$ optimization method and was implemented in this research. The objective of $H_2$ optimization criterion is to reduce the total vibration energy of the system for overall frequencies. An objective function, considering the elbow joint angle, ${ heta}_2$, tremor suppression as the main goal, was selected. The optimization was done by minimization of this objective function. The optimal system, including the absorber, performance was analyzed in both time and frequency domains. Implementing the optimal absorber, the frequency response amplitude of ${ heta}_2$ was reduced by more than 98% and 80% at the first and second natural frequencies of the primary system, respectively. A reduction of more than 94% and 78%, was observed for the shoulder joint angle, ${ heta}_1$. The objective function also decreased by more than 46%. Then, two types of random inputs were considered. For the first type, ${ heta}_1$ and ${ heta}_2$ revealed 60% and 39% reduction in their rms values, whereas for the second type, 33% and 50% decrease was observed.