Our major goal is to account for some simple digit-recall data with a theory that integrates two models from two scientific traditions. The random-sampling model, founded in the memory and attention literature, holds that (1) stimulus features are randomly sampled throughout the course of stimulus presence and (2) proportion correct recall is equal to the ratio of sampled features to total features. The linear-filter model, founded in the vision and sensation literature, holds that the initial stages of the visual system act as a low-pass temporal filter on the input stimulus, resulting in a time-varying sensory response in the nervous system. We report two experiments in which a variable-duration, masked, four-digit string had to be immediately recalled. Experiment 1 was designed principally to replicate past data confirming the basic randomsampling model. Like others, we were able to confirm the model only by endowing it with an additional processing-delay assumption: that feature sampling does not begin until the stimulus has been physically present for some minimal duration. Experiment 2 was an extension of Experiment 1 in which the target stimulus was preceded, 250 msec prior to its onset, by a 50-msec pre-presentation of the same stimulus called a prime. The Experiment 2 results allowed the following conclusions. First, the initial processing delay found in Experiment 1 is immutably tied to stimulus onset; that is, if there are two stimulus onsets, separated even briefly in time, there are two associated processing delays. Second, processing rate is essentially unaffected by the prime's presentation. Third, being presented with a 50-msec prime is equivalent, in terms ofmemory performance, to increasing unprimed stimulus duration by approximately 30 msec; the prime can thus said to be worth 30 msec of additional exposure duration. This third conclusion seems superficially paradoxical, in the sense that one would expect that having seen a 50-msec prime would be equivalent to increasing exposure duration by at least the same 50 msec. However, both the initial processing delays and the 30-msec prime's worth are natural consequences of our theory that conjoins the random-sampling model with the linear-filter model. Two fundamental questions in perception are, What is the nature of information acquisition that follows the onset of a stimulus, and how is such information acquisition influenced by other priming stimuli presented prior to the stimulus? In this article, we report two experiments that bear on both of these questions as they apply to a digitrecall task in which a four-digit string is presented for varying durations to an observer who must immediately recall as many of the digits as possible.Such tasks have often been accounted for by one form or another of a random-sampling model. Variants of random-sampling models have long enjoyed popularity, both in the learning literature (e.g., Neimark & Estes, 1967) and in the attention and perception literature (e.g., This research was supported by an NIMH gran...