A gentle introduction to the Poisson process assumptions in a probability course
Why this work is in the frame
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Bibliographic record
Abstract
A first glance by probability students at the assumptions underlying the Poisson process can lead to confusion and possibly anxiety. Although attempts are usually made to describe the assumptions in words, the motivation behind the assumptions is often unclear, and the eventual derivation of the Poisson distribution formulae can then appear to be quite magical. In fact, it is a beautiful result, and the Bernoulli process provides a way for more students to be able to appreciate all aspects of a Poisson process model and its derivation. A small number of authors have been using the Bernoulli process as an approximation to the Poisson process; the present paper adopts their approach and outlines a teaching strategy that leads from the more naturally defined Bernoulli process assumptions to the Poisson process assumptions.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it