Before revision:  The distribution of the equilibrium of this extended model is analyzed . Explicit expressions are obtained for the first two moments of the number of mRNAs and proteins at equilibrium  generalizing some classical formulas.
After revision:  The distribution of the equilibrium of this extended model is analyzed . Explicit expressions are obtained for the first two moments of the number of mRNAs and proteins at equilibrium are derived, generalizing some classical formulas.