The ability to simultaneously measure mRNA abundance for large number of genes has revolutionized biological research by allowing statistical analysis of global gene-expression data. Large-scale gene-expression data sets have been analyzed in order to identify the probability distributions of gene expression levels (or transcript copy numbers) in eukaryotic cells. Determining such function(s) may provide a theoretical basis for accurately counting all expressed genes in a given cell and for understanding gene expression control. Using the gene-expression libraries derived from yeast cells and from different human cell tissues we found that all observed gene expression levels data appear to follow a Pareto-like skewed frequency distribution. We produced a the skewed probability function, called the Binomial Differential distribution, that accounts for many rarely transcribed genes in a single cell. We also developed a novel method for estimating and removing major experimental errors and redundancies from the Serial Analysis Gene Expression (SAGE) data sets. We successfully applied this method to the yeast transcriptome. A “basal” random transcription mechanism for all protein-coding genes in every eukaryotic cell type is predicted.