In order to grow and replicate, living cells must express a diverse array of proteins, but the process by which proteins are made includes a great deal of inherent randomness. Understanding this randomness—whether it arises from the discrete stochastic nature of chemical reactivity (“intrinsic” noise), or from cell-to-cell variability in the concentrations of molecules involved in gene expression or the timings of important cell-cycle events like DNA replication or cell division (“extrinsic” noise)—remains a challenge. In this article we analyze a model of gene expression that accounts for several extrinsic sources of noise, including those associated with chromosomal replication, cell division, and variability in the numbers of RNA polymerase, ribonuclease E, and ribosomes. We then attempt to fit our model to a large proteomics and transcriptomics data set, and find that only through the introduction of a few key correlations among the extrinsic noise sources can we accurately recapitulate the experimental data. These include significant correlations between the rate of mRNA degradation (mediated by ribonuclease E) and the rates of both transcription (RNA polymerase) and translation (ribosomes), and strikingly, an anticorrelation between the transcription and translation rates themselves.