[en] Highlights: • Dipole moment, polarizability and self-polarization effect (SPE) of doped quantum dot are studied. • The dot is subjected to Gaussian white noise. • Special emphasis is put on role of binding energy (BE). • Interplay between noise and BE prominently affects above properties. Present study inspects the profiles of electric dipole moment (DPM), polarizability (${\alpha }_p$) and self-polarization effect (SPE) of doped GaAs quantum dots (QDs) in presence of noise. Special stress has been given on understanding the role of binding energy (BE). Noise term maintains a Gaussian white character and it has been introduced to the system additively and multiplicatively. Application of noise affects the above properties noticeably with conspicuous dependence on the pathway of application. The findings reveal feasible routes to tune the above aspects of doped QD system through expedient adjustment of BE, particularly in presence of noise.