A simplified mathematical model of gene transcription is presented based on a system of coupled chemical reactions and a corresponding set of stochastic equations similar to those used in enzyme kinetics theory. The steady state distribution for the model is derived and its usefulness illustrated with an example of the model parameters estimation using sparse time course data on L1 retrotransposon expression kinetics. The issue of model validation is also discussed and a simple validation procedure for the estimated model is devised comparing model predicted values with the laboratory data via the standard Bayesian techniques utilizing modern Markov-Chain Monte-Carlo methodology.