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:  A convergence result to equilibrium for the process associated to the number of proteins and mRNAs is proved and a representation of this equilibrium as a functional of a Poisson process in an extended state space is obtained . Explicit expressions are obtained for the first two moments of the number of mRNAs and proteins at equilibrium generalizing some classical formulas.