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Gene regulation in a cellular environment is a stochastic phenomenon leading to a large variability in mRNAs and protein numbers that are often produced in bursts. The regulation leading to varied protein dynamics can be ascribed to transcriptional or post-transcriptional mechanisms. In transcriptional regulation, the gene dynamically switches between an active and an inactive state, while in the post-transcriptional regulation small RNAs tune the activity of mRNAs. In either scenario, it is possible to calculate the time-dependent prob