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Probability Distributions Arising in Connection with the Inspection Paradox for Bernoulli Trials
School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
- 1 School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
- 2 School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
- 3 School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
- 4 School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA
Open Journal of Statistics·Volume 13 (2023)·Pages 769–777·Published 13 November 2023·DOI10.4236/ojs.2023.136038
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Abstract
In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.
KeywordsInspection ParadoxInterarrival TimeBernoulli TrialRenewal ProcessWaiting Time
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