Before revision:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP),  to examine the transition events from low to high concentration state under the influence of L\'evy noise.
After revision:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), to examine the likelihood for transcriptions: The mean time scale for the system exits the low concentration state (the longer the exit time, the less likely for transcription) and the switch probability from low concentration states to high concentration state under the influence of L\'evy noise.