We describe a model of the response of a single visual channel to weak test lights. We assume that the initial channel response may be approximated as a linear filter whose output is sampled at random times. At each sample time there is some probability (increasing with the size of the filter response) that a detection event is generated. The detection events form the basis of the observer's detection and duration discrimination judgments. We derive the statistics of the detection events and empirical tests of the model. Assuming the probability of a detection event to be negligible in the absence of a signal, we derive an exact prediction of the form of the psychometric function for detection. Second, assuming that duration discrimination of weak test lights is based solely on the temporal separation of detection events, we predict the exact form of detection/discrimination performance. Third, assuming that the observer's response is initiated by the first detection event, we derive the form of the cumulative reaction time distribution.