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Time-of-flight (TOF) positron emission tomography (PET) has the potential to improve signal-to-noise ratio (SNR). In the literature, this improvement has been estimated as proportional to the square root of D/Δx, where D is the radial dimension of the object to be imaged, and Δx is the spatial uncertainty associated with the time resolution of the scanner. This estimate does not include the effect of the randoms. In this paper we discuss the role of random coincidence in TOF PET; in particular, the improvement in SNR due to random reduction in TOF PET. We introduce and discuss a simple model for this improvement, modify the traditional estimate for SNR gain, and compare it to experimental data from a Siemens Hi-Rez PET scanner with TOF capability.