Before revision:  We also derive the analytic steady-state distributions of the protein abundance  for both the discrete chemical master equation model and its two macroscopic limits . Furthermore, we ] obtain the analytic time-dependent distribution of the protein concentration for the classical Friedman-Cai-Xie random bursting model   .
After revision:  We also derive the analytic steady-state distributions of the protein abundance for both the discrete chemical master equation model and its two macroscopic limits , generalizing the results obtained in ] obtain the analytic time-dependent distribution of the protein concentration for the classical Friedman-Cai-Xie random bursting model .