Single-cell RNA sequencing is a powerful tool for exploring gene expression heterogeneity, but the results may be obscured by technical noise inherent in the experimental procedure. Here we introduce a novel parametrisation of sc-RNA data, giving estimates of the probability of activation of a gene and its peak transcription rate, which are agnostic about the mechanism underlying the fluctuations in the counts. Applying this approach to single cell mRNA counts across different tissues of adult mice, we find that peak transcription levels are approximately constant across different tissue types, in contrast to the gene expression probabilities which are, for many genes, markedly different. Many genes are only observed in a small fraction of cells. An investigation of correlation between genes activities shows that this is primarily due to temporal intermittency of transcription, rather than some genes being expressed in specialised cell types. Both the probability of activation and the peak transcription rate have a very wide ranges of values, with a probability density function well approximated by a power law. Taken together, our results indicate that the peak rate of transcription is a persistent property of a gene, and that differences in gene expression are modulated by temporal intermittency of the transcription.