Before revision:   In this paper, we analytically calculate the noise in mRNA and protein levels and also the probability distribution of mRNA numbers exactly with the binding event of RNAP in gene transcription process.
After 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. In this paper, we analytically calculate the noise in mRNA and protein levels and also the probability distribution of mRNA numbers exactly with the binding event of RNAP in gene transcription process.