Abstract
The well-known inspection paradox of renewal theory states that, in expectation, the inspection interval is larger than a common renewal interval, in general. For a random inspection time, which includes the deterministic case, and a delayed renewal process, representations of the expected length of an inspection interval and related inequalities in terms of covariances are shown. Datasets of eruption times of Beehive Geyser and Riverside Geyser in Yellowstone National Park, as well as several distributional examples, illustrate the findings.
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