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Variations in the spatial density of carbon nanotubes (CNTs), resulting from the lack of precise control over CNT positioning during chemical synthesis, is a major hurdle to the scalability of carbon nanotube field effect transistor (CNFET) circuits. Such CNT density variations can lead to non-functional CNFET circuits. This paper presents a probabilistic framework for modeling the CNT count distribution contained in a CNFET of given width, and establishes the accuracy of the model using experimental data obtained from CNT growth. Using this model, we estimate the impact of CNT density variations on the yield of CNFET very large-scale integrated circuits. Our estimation results demonstrate that CNT density variations can significantly degrade the yield of CNFETs, and can be a major concern for scaled CNFET circuits. Finally, we analyze the impact of CNT correlation (i.e., correlation of CNT count between CNFETs) that exists in CNT growth, and demonstrate how the yield of a CNFET storage circuit (primarily limited by its noise immunity) can be significantly improved by taking advantage of such correlation.