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In this paper, we derive the probability mass function (PMF) and the cumulative mass function (CMF) of the sum of discrete independent and identically distributed random variables. As an application of the PMF and CMF, we analyze the missed-detection, false-alarm, and overall error probabilities of cooperative spectrum sensing with any numbers of quantization levels and any quantization thresholds in a closed form. Computer simulation results match the analysis perfectly. In addition, centralized and distributed threshold selections are discussed.