We present an analytical framework describing the steady-state distribution of protein concentration in live cells, considering that protein production occurs in random bursts with an exponentially distributed number of molecules. We extend this framework for cases of transcription autoregulation and noise propagation in a simple genetic network. This model allows for the extraction of kinetic parameters of gene expression from steady-state distributions of protein concentration in a cell population, which are available from single cell data obtained by flow cytometry or fluorescence microscopy.