Recent advances in technology have enabled biologists to investigate gene expression in single cells. In such experimental investigations, it has been demonstrated that the numbers of mRNA and protein molecules expressed from a gene in a single cell are stochastic processes. While the stochasticity in gene expression, which is also referred to as gene expression noise by biologists, has recently attracted much attention of biologists, less attention has been paid to analyze the stochastic nature of gene expression based on a computational model. In this paper, we first analyze the mean and variance of the mRNA and protein molecules expressed from a gene based on a stochastic model. In this stochastic model, a gene randomly switches between two states: activated and repressed states and transcribed with different probability rates in these two states. We then investigate the estimation of model parameters based on the observed numbers of mRNA and protein molecules. Our computational approach can predict the behavior of gene expression in single cells.