Before revision:  The  binding event of RNAP to the active state of the gene is an probabilistic process and therefore introduces noise in the protein levels.
After revision:  The RNAP molecules can bind the gene only after the promoter gets activated by transcription factors. Several transcription factors bind the promoter to put the gene in the active state. The gene turns into the inactive state as the bound transcription factors leave the promoter. During the active period of the gene, many RNAP molecules transcribe the gene to synthesize the mRNA. The binding event of RNAP to the active state of the gene is an probabilistic process and therefore introduces noise in the protein levels.