The origin of stochastic fluctuations in gene expression has received considerable attention recently. Fluctuations in gene expression are particularly pronounced in cellular systems because of the small copy number of species undergoing transitions between discrete chemical states and the small size of biological compartments. In this paper, we propose a stochastic model for gene expression regulation including several binding sites, considering elementary reactions only. The model is used to investigate the role of cooperativity on the intrinsic fluctuations of gene expression by means of master-equation formalism. We found that the Hill coefficient and the level of noise increase as the interaction energy between activators increases. Additionally, we show that the model allows one to distinguish between two cooperative binding mechanisms.