Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional pro-cesses downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. We derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations on gene segments, as well as of total nascent RNA on a gene. We also obtain exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions fortotal numbers of nascent and mature RNA. Our results, which are veried by stochastic simulation,uncover the explicit dependence of the statistics of both types of RNA on transcriptional parametersand potentially provide a means to estimate parameter values from experimental data.