# Precommitted Finite Intervals, Pointwise Coverage and Selection Boundaries

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations · 2026-10-15 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

Field order uses a source-bound presentation supplement; canonical JSONL and mathematical answers are unchanged.

[Field-order and source-binding data](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[1/3, 2/3], [2/3, 1/3]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[1/3, 2/3], [2/3, 1/3]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[1/3, 2/3], [2/3, 1/3]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0001/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 2. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[2/4, 2/4], [2/4, 2/4]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[1/2, 1/2], [1/2, 1/2]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[1/2, 1/2], [1/2, 1/2]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0002/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 3. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[3/5, 2/5], [2/5, 3/5]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[3/5, 2/5], [2/5, 3/5]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[3/5, 2/5], [2/5, 3/5]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0003/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 4. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[4/6, 2/6], [2/6, 4/6]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[2/3, 1/3], [1/3, 2/3]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[2/3, 1/3], [1/3, 2/3]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0004/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 5. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[5/7, 2/7], [2/7, 5/7]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[5/7, 2/7], [2/7, 5/7]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[5/7, 2/7], [2/7, 5/7]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0005/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 6. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[6/8, 2/8], [2/8, 6/8]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[3/4, 1/4], [1/4, 3/4]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[3/4, 1/4], [1/4, 3/4]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0006/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 7. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[7/9, 2/9], [2/9, 7/9]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[7/9, 2/9], [2/9, 7/9]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[7/9, 2/9], [2/9, 7/9]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0007/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 8. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[8/10, 2/10], [2/10, 8/10]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[4/5, 1/5], [1/5, 4/5]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[4/5, 1/5], [1/5, 4/5]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0008/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 9. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[9/11, 2/11], [2/11, 9/11]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[9/11, 2/11], [2/11, 9/11]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[9/11, 2/11], [2/11, 9/11]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0009/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 10. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[10/12, 2/12], [2/12, 10/12]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[5/6, 1/6], [1/6, 5/6]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[5/6, 1/6], [1/6, 5/6]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0010/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 11. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[11/13, 2/13], [2/13, 11/13]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[11/13, 2/13], [2/13, 11/13]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[11/13, 2/13], [2/13, 11/13]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0011/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 12. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[12/14, 2/14], [2/14, 12/14]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[6/7, 1/7], [1/7, 6/7]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[6/7, 1/7], [1/7, 6/7]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0012/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 13. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[13/15, 2/15], [2/15, 13/15]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[13/15, 2/15], [2/15, 13/15]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[13/15, 2/15], [2/15, 13/15]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0013/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 14. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[14/16, 2/16], [2/16, 14/16]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[7/8, 1/8], [1/8, 7/8]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[7/8, 1/8], [1/8, 7/8]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0014/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 15. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[15/17, 2/17], [2/17, 15/17]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[15/17, 2/17], [2/17, 15/17]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[15/17, 2/17], [2/17, 15/17]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0015/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 16. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[16/18, 2/18], [2/18, 16/18]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[8/9, 1/9], [1/9, 8/9]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[8/9, 1/9], [1/9, 8/9]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0016/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 17. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[17/19, 2/19], [2/19, 17/19]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[17/19, 2/19], [2/19, 17/19]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[17/19, 2/19], [2/19, 17/19]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0017/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 18. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[18/20, 2/20], [2/20, 18/20]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[9/10, 1/10], [1/10, 9/10]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[9/10, 1/10], [1/10, 9/10]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0018/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 19. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[19/21, 2/21], [2/21, 19/21]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[19/21, 2/21], [2/21, 19/21]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[19/21, 2/21], [2/21, 19/21]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0019/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 20. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[20/22, 2/22], [2/22, 20/22]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[10/11, 1/11], [1/11, 10/11]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[10/11, 1/11], [1/11, 10/11]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0020/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 21. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[21/23, 2/23], [2/23, 21/23]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[21/23, 2/23], [2/23, 21/23]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[21/23, 2/23], [2/23, 21/23]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0021/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 22. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[22/24, 2/24], [2/24, 22/24]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[11/12, 1/12], [1/12, 11/12]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[11/12, 1/12], [1/12, 11/12]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0022/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 23. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[23/25, 2/25], [2/25, 23/25]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[23/25, 2/25], [2/25, 23/25]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[23/25, 2/25], [2/25, 23/25]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0023/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 24. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[24/26, 2/26], [2/26, 24/26]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[12/13, 1/13], [1/13, 12/13]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[12/13, 1/13], [1/13, 12/13]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0024/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 25. A Complete Precommitted Interval Procedure Keeps Every Probability Alignment

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[25/27, 2/27], [2/27, 25/27]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (theta_values, samples, aligned_closed_intervals, aligned_probability_rows, procedure_qualified, qualification_statement).

Intervals align with samples; probability rows align with theta and samples. The procedure is total, precommitted and independent of the unknown theta. A separate unadopted frozen-helper sorting diagnostic concerns cross-digit theta values; all current rows use[0,1].

View answer and explanation([0, 1], [a, b], [[0, 0], [1, 1]], [[25/27, 2/27], [2/27, 25/27]], Yes, total_precommitted_theta_independent_interval_procedure)

Qualify all closed endpoints and the entire normalized law for each theta. Preserve sample/interval and theta/row associations under canonical ordering. The procedure may depend on data but not on the unknown true theta. This is finite-model qualification, not an asymptotic coverage theorem. The exact result, retaining the requested order, is ([0, 1], [a, b], [[0, 0], [1, 1]], [[25/27, 2/27], [2/27, 25/27]], Yes, total_precommitted_theta_independent_interval_procedure).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0025/)

Confidence-interval coverage in a finite model · qf-mod49-ci-procedure-qualification · candidate





## 26. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[1/3, 2/3], [2/3, 1/3]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 1/3], [1, 1/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 1/3], [1, 1/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0026/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 27. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[2/4, 2/4], [2/4, 2/4]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 1/2], [1, 1/2]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 1/2], [1, 1/2]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0027/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 28. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[3/5, 2/5], [2/5, 3/5]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 3/5], [1, 3/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 3/5], [1, 3/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0028/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 29. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[4/6, 2/6], [2/6, 4/6]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 2/3], [1, 2/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 2/3], [1, 2/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0029/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 30. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[5/7, 2/7], [2/7, 5/7]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 5/7], [1, 5/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 5/7], [1, 5/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0030/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 31. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[6/8, 2/8], [2/8, 6/8]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 3/4], [1, 3/4]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 3/4], [1, 3/4]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0031/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 32. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[7/9, 2/9], [2/9, 7/9]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 7/9], [1, 7/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 7/9], [1, 7/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0032/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 33. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[8/10, 2/10], [2/10, 8/10]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 4/5], [1, 4/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 4/5], [1, 4/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0033/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 34. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[9/11, 2/11], [2/11, 9/11]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 9/11], [1, 9/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 9/11], [1, 9/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0034/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 35. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[10/12, 2/12], [2/12, 10/12]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 5/6], [1, 5/6]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 5/6], [1, 5/6]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0035/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 36. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[11/13, 2/13], [2/13, 11/13]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 11/13], [1, 11/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 11/13], [1, 11/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0036/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 37. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[12/14, 2/14], [2/14, 12/14]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 6/7], [1, 6/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 6/7], [1, 6/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0037/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 38. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[13/15, 2/15], [2/15, 13/15]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 13/15], [1, 13/15]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 13/15], [1, 13/15]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0038/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 39. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[14/16, 2/16], [2/16, 14/16]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 7/8], [1, 7/8]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 7/8], [1, 7/8]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0039/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 40. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[15/17, 2/17], [2/17, 15/17]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 15/17], [1, 15/17]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 15/17], [1, 15/17]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0040/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 41. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[16/18, 2/18], [2/18, 16/18]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 8/9], [1, 8/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 8/9], [1, 8/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0041/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 42. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[17/19, 2/19], [2/19, 17/19]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 17/19], [1, 17/19]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 17/19], [1, 17/19]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0042/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 43. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[18/20, 2/20], [2/20, 18/20]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 9/10], [1, 9/10]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 9/10], [1, 9/10]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0043/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 44. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[19/21, 2/21], [2/21, 19/21]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 19/21], [1, 19/21]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 19/21], [1, 19/21]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0044/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 45. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[20/22, 2/22], [2/22, 20/22]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 10/11], [1, 10/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 10/11], [1, 10/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0045/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 46. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[21/23, 2/23], [2/23, 21/23]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 21/23], [1, 21/23]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 21/23], [1, 21/23]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0046/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 47. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[22/24, 2/24], [2/24, 22/24]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 11/12], [1, 11/12]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 11/12], [1, 11/12]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0047/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 48. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[23/25, 2/25], [2/25, 23/25]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 23/25], [1, 23/25]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 23/25], [1, 23/25]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0048/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 49. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[24/26, 2/26], [2/26, 24/26]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 12/13], [1, 12/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 12/13], [1, 12/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0049/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 50. Coverage Is a Repeated-Sampling Probability at Each Fixed Theta

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[25/27, 2/27], [2/27, 25/27]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. Give (pointwise_coverage_table, coverage_definition, frequentist_scope).

View answer and explanation([[0, 25/27], [1, 25/27]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)

For each fixed theta sum exactly P_theta(x) over all samples whose reported interval contains theta, including endpoints. Keep the full pointwise table. This is not posterior probability for theta after observing one sample. The exact result, retaining the requested order, is ([[0, 25/27], [1, 25/27]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0050/)

Confidence-interval coverage in a finite model · qf-mod49-ci-pointwise-coverage · candidate





## 51. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[1/3, 2/3], [2/3, 1/3]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=1/3. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 1/3], [1, 1/3]], 1/3, 1/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 1/3], [1, 1/3]], 1/3, 1/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0051/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 52. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[2/4, 2/4], [2/4, 2/4]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=2/4. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 1/2], [1, 1/2]], 1/2, 1/2, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 1/2], [1, 1/2]], 1/2, 1/2, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0052/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 53. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[3/5, 2/5], [2/5, 3/5]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=3/5. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 3/5], [1, 3/5]], 3/5, 3/5, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 3/5], [1, 3/5]], 3/5, 3/5, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0053/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 54. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[4/6, 2/6], [2/6, 4/6]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=4/6. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 2/3], [1, 2/3]], 2/3, 2/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 2/3], [1, 2/3]], 2/3, 2/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0054/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 55. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[5/7, 2/7], [2/7, 5/7]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=5/7. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 5/7], [1, 5/7]], 5/7, 5/7, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 5/7], [1, 5/7]], 5/7, 5/7, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0055/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 56. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[6/8, 2/8], [2/8, 6/8]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=1/3. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 3/4], [1, 3/4]], 3/4, 1/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 3/4], [1, 3/4]], 3/4, 1/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0056/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 57. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[7/9, 2/9], [2/9, 7/9]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=2/4. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 7/9], [1, 7/9]], 7/9, 1/2, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 7/9], [1, 7/9]], 7/9, 1/2, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0057/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 58. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[8/10, 2/10], [2/10, 8/10]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=3/5. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 4/5], [1, 4/5]], 4/5, 3/5, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 4/5], [1, 4/5]], 4/5, 3/5, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0058/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 59. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[9/11, 2/11], [2/11, 9/11]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=4/6. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 9/11], [1, 9/11]], 9/11, 2/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 9/11], [1, 9/11]], 9/11, 2/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0059/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 60. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[10/12, 2/12], [2/12, 10/12]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=5/7. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 5/6], [1, 5/6]], 5/6, 5/7, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 5/6], [1, 5/6]], 5/6, 5/7, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0060/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 61. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[11/13, 2/13], [2/13, 11/13]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=1/3. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 11/13], [1, 11/13]], 11/13, 1/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 11/13], [1, 11/13]], 11/13, 1/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0061/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 62. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[12/14, 2/14], [2/14, 12/14]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=2/4. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 6/7], [1, 6/7]], 6/7, 1/2, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 6/7], [1, 6/7]], 6/7, 1/2, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0062/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 63. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[13/15, 2/15], [2/15, 13/15]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=3/5. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 13/15], [1, 13/15]], 13/15, 3/5, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 13/15], [1, 13/15]], 13/15, 3/5, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0063/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 64. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[14/16, 2/16], [2/16, 14/16]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=4/6. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 7/8], [1, 7/8]], 7/8, 2/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 7/8], [1, 7/8]], 7/8, 2/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0064/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 65. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[15/17, 2/17], [2/17, 15/17]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=5/7. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 15/17], [1, 15/17]], 15/17, 5/7, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 15/17], [1, 15/17]], 15/17, 5/7, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0065/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 66. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[16/18, 2/18], [2/18, 16/18]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=1/3. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 8/9], [1, 8/9]], 8/9, 1/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 8/9], [1, 8/9]], 8/9, 1/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0066/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 67. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[17/19, 2/19], [2/19, 17/19]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=2/4. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 17/19], [1, 17/19]], 17/19, 1/2, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 17/19], [1, 17/19]], 17/19, 1/2, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0067/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 68. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[18/20, 2/20], [2/20, 18/20]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=3/5. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 9/10], [1, 9/10]], 9/10, 3/5, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 9/10], [1, 9/10]], 9/10, 3/5, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0068/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 69. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[19/21, 2/21], [2/21, 19/21]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=4/6. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 19/21], [1, 19/21]], 19/21, 2/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 19/21], [1, 19/21]], 19/21, 2/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0069/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 70. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[20/22, 2/22], [2/22, 20/22]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=5/7. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 10/11], [1, 10/11]], 10/11, 5/7, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 10/11], [1, 10/11]], 10/11, 5/7, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0070/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 71. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[21/23, 2/23], [2/23, 21/23]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=1/3. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 21/23], [1, 21/23]], 21/23, 1/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 21/23], [1, 21/23]], 21/23, 1/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0071/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 72. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[22/24, 2/24], [2/24, 22/24]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=2/4. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 11/12], [1, 11/12]], 11/12, 1/2, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 11/12], [1, 11/12]], 11/12, 1/2, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0072/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 73. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[23/25, 2/25], [2/25, 23/25]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=3/5. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 23/25], [1, 23/25]], 23/25, 3/5, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 23/25], [1, 23/25]], 23/25, 3/5, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0073/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 74. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[24/26, 2/26], [2/26, 24/26]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=4/6. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 12/13], [1, 12/13]], 12/13, 2/3, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 12/13], [1, 12/13]], 12/13, 2/3, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0074/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 75. A Uniform Coverage Target Is Checked against the Minimum, Not an Average

Use complete theta values=[0, 1], samples=[a, b], theta/sample-aligned probability rows=[[25/27, 2/27], [2/27, 25/27]], and sample-aligned closed intervals=[[0, 0], [1, 1]]. The interval procedure is total, precommitted and independent of the unknown theta. The declared target is=5/7. Give (pointwise_coverage_table, minimum_coverage, target, uniform_target_met, minimum_definition).

View answer and explanation([[0, 25/27], [1, 25/27]], 25/27, 5/7, Yes, worst_case_is_minimum_over_finite_theta)

Calculate every pointwise coverage and take the minimum over the finite theta carrier. Compare that exact minimum with the target. Weighted average coverage cannot substitute for this uniform criterion. The exact result, retaining the requested order, is ([[0, 25/27], [1, 25/27]], 25/27, 5/7, Yes, worst_case_is_minimum_over_finite_theta).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0075/)

Confidence-interval coverage in a finite model · qf-mod49-ci-worst-case-coverage · candidate





## 76. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=average_only and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[1,3],[2,3]],[[2,3],[1,3]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]}. Give (mode, pointwise_coverage_table, theta_weights, weighted_average, minimum_coverage, target, distinct_coverages, average_strictly_above_minimum, average_masks_target_failure, average_implies_uniform_target_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0076/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 77. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=posterior_confusion and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[2,4],[2,4]],[[2,4],[2,4]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"}. Give (mode, observed_sample, posterior_by_theta, pointwise_coverage_table, posterior_equals_coverage_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(posterior_confusion, b, [1/2, 1/2], [[0, 1/2], [1, 1/2]], No, posterior_given_observed_data_is_not_frequentist_coverage)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (posterior_confusion, b, [1/2, 1/2], [[0, 1/2], [1, 1/2]], No, posterior_given_observed_data_is_not_frequentist_coverage).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0077/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 78. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=ignored_selection and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[3,5],[2,5]],[[2,5],[3,5]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}. Give (mode, selected_samples, unconditional_coverage_table, selected_mass_and_conditional_coverage_by_theta, unchanged_coverage_without_recomputation_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(ignored_selection, [a], [[0, 3/5], [1, 3/5]], [[0, 3/5, 1], [1, 2/5, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (ignored_selection, [a], [[0, 3/5], [1, 3/5]], [[0, 3/5, 1], [1, 2/5, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0078/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 79. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[4,6],[2,6]],[[2,6],[4,6]]],"intervals":[[4,3],[4,4]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0079/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 80. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=average_only and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[5,7],[2,7]],[[2,7],[5,7]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]}. Give (mode, pointwise_coverage_table, theta_weights, weighted_average, minimum_coverage, target, distinct_coverages, average_strictly_above_minimum, average_masks_target_failure, average_implies_uniform_target_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0080/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 81. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=posterior_confusion and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[6,8],[2,8]],[[2,8],[6,8]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"}. Give (mode, observed_sample, posterior_by_theta, pointwise_coverage_table, posterior_equals_coverage_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(posterior_confusion, b, [1/4, 3/4], [[0, 3/4], [1, 3/4]], No, posterior_given_observed_data_is_not_frequentist_coverage)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (posterior_confusion, b, [1/4, 3/4], [[0, 3/4], [1, 3/4]], No, posterior_given_observed_data_is_not_frequentist_coverage).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0081/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 82. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=ignored_selection and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[7,9],[2,9]],[[2,9],[7,9]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}. Give (mode, selected_samples, unconditional_coverage_table, selected_mass_and_conditional_coverage_by_theta, unchanged_coverage_without_recomputation_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(ignored_selection, [a], [[0, 7/9], [1, 7/9]], [[0, 7/9, 1], [1, 2/9, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (ignored_selection, [a], [[0, 7/9], [1, 7/9]], [[0, 7/9, 1], [1, 2/9, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0082/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 83. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[8,10],[2,10]],[[2,10],[8,10]]],"intervals":[[8,7],[8,8]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0083/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 84. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=average_only and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[9,11],[2,11]],[[2,11],[9,11]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]}. Give (mode, pointwise_coverage_table, theta_weights, weighted_average, minimum_coverage, target, distinct_coverages, average_strictly_above_minimum, average_masks_target_failure, average_implies_uniform_target_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0084/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 85. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=posterior_confusion and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[10,12],[2,12]],[[2,12],[10,12]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"}. Give (mode, observed_sample, posterior_by_theta, pointwise_coverage_table, posterior_equals_coverage_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(posterior_confusion, b, [1/6, 5/6], [[0, 5/6], [1, 5/6]], No, posterior_given_observed_data_is_not_frequentist_coverage)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (posterior_confusion, b, [1/6, 5/6], [[0, 5/6], [1, 5/6]], No, posterior_given_observed_data_is_not_frequentist_coverage).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0085/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 86. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=ignored_selection and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[11,13],[2,13]],[[2,13],[11,13]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}. Give (mode, selected_samples, unconditional_coverage_table, selected_mass_and_conditional_coverage_by_theta, unchanged_coverage_without_recomputation_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(ignored_selection, [a], [[0, 11/13], [1, 11/13]], [[0, 11/13, 1], [1, 2/13, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (ignored_selection, [a], [[0, 11/13], [1, 11/13]], [[0, 11/13, 1], [1, 2/13, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0086/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 87. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[12,14],[2,14]],[[2,14],[12,14]]],"intervals":[[12,11],[12,12]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0087/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 88. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=average_only and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[13,15],[2,15]],[[2,15],[13,15]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]}. Give (mode, pointwise_coverage_table, theta_weights, weighted_average, minimum_coverage, target, distinct_coverages, average_strictly_above_minimum, average_masks_target_failure, average_implies_uniform_target_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0088/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 89. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=posterior_confusion and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[14,16],[2,16]],[[2,16],[14,16]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"}. Give (mode, observed_sample, posterior_by_theta, pointwise_coverage_table, posterior_equals_coverage_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(posterior_confusion, b, [1/8, 7/8], [[0, 7/8], [1, 7/8]], No, posterior_given_observed_data_is_not_frequentist_coverage)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (posterior_confusion, b, [1/8, 7/8], [[0, 7/8], [1, 7/8]], No, posterior_given_observed_data_is_not_frequentist_coverage).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0089/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 90. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=ignored_selection and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[15,17],[2,17]],[[2,17],[15,17]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}. Give (mode, selected_samples, unconditional_coverage_table, selected_mass_and_conditional_coverage_by_theta, unchanged_coverage_without_recomputation_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(ignored_selection, [a], [[0, 15/17], [1, 15/17]], [[0, 15/17, 1], [1, 2/17, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (ignored_selection, [a], [[0, 15/17], [1, 15/17]], [[0, 15/17, 1], [1, 2/17, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0090/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 91. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[16,18],[2,18]],[[2,18],[16,18]]],"intervals":[[16,15],[16,16]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0091/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 92. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=average_only and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[17,19],[2,19]],[[2,19],[17,19]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]}. Give (mode, pointwise_coverage_table, theta_weights, weighted_average, minimum_coverage, target, distinct_coverages, average_strictly_above_minimum, average_masks_target_failure, average_implies_uniform_target_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0092/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 93. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=posterior_confusion and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[18,20],[2,20]],[[2,20],[18,20]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"}. Give (mode, observed_sample, posterior_by_theta, pointwise_coverage_table, posterior_equals_coverage_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(posterior_confusion, b, [1/10, 9/10], [[0, 9/10], [1, 9/10]], No, posterior_given_observed_data_is_not_frequentist_coverage)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (posterior_confusion, b, [1/10, 9/10], [[0, 9/10], [1, 9/10]], No, posterior_given_observed_data_is_not_frequentist_coverage).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0093/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 94. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=ignored_selection and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[19,21],[2,21]],[[2,21],[19,21]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}. Give (mode, selected_samples, unconditional_coverage_table, selected_mass_and_conditional_coverage_by_theta, unchanged_coverage_without_recomputation_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(ignored_selection, [a], [[0, 19/21], [1, 19/21]], [[0, 19/21, 1], [1, 2/21, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (ignored_selection, [a], [[0, 19/21], [1, 19/21]], [[0, 19/21, 1], [1, 2/21, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0094/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 95. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[20,22],[2,22]],[[2,22],[20,22]]],"intervals":[[20,19],[20,20]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0095/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 96. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=average_only and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[21,23],[2,23]],[[2,23],[21,23]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]}. Give (mode, pointwise_coverage_table, theta_weights, weighted_average, minimum_coverage, target, distinct_coverages, average_strictly_above_minimum, average_masks_target_failure, average_implies_uniform_target_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0096/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 97. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=posterior_confusion and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[22,24],[2,24]],[[2,24],[22,24]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"}. Give (mode, observed_sample, posterior_by_theta, pointwise_coverage_table, posterior_equals_coverage_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(posterior_confusion, b, [1/12, 11/12], [[0, 11/12], [1, 11/12]], No, posterior_given_observed_data_is_not_frequentist_coverage)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (posterior_confusion, b, [1/12, 11/12], [[0, 11/12], [1, 11/12]], No, posterior_given_observed_data_is_not_frequentist_coverage).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0097/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 98. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=ignored_selection and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[23,25],[2,25]],[[2,25],[23,25]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}. Give (mode, selected_samples, unconditional_coverage_table, selected_mass_and_conditional_coverage_by_theta, unchanged_coverage_without_recomputation_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(ignored_selection, [a], [[0, 23/25], [1, 23/25]], [[0, 23/25, 1], [1, 2/25, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (ignored_selection, [a], [[0, 23/25], [1, 23/25]], [[0, 23/25, 1], [1, 2/25, 0]], No, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0098/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 99. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[24,26],[2,26]],[[2,26],[24,26]]],"intervals":[[24,23],[24,24]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0099/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate





## 100. Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Use mode=average_only and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[25,27],[2,27]],[[2,27],[25,27]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]}. Give (mode, pointwise_coverage_table, theta_weights, weighted_average, minimum_coverage, target, distinct_coverages, average_strictly_above_minimum, average_masks_target_failure, average_implies_uniform_target_claim, boundary).

The four modes have11/6/6/4 fields. Conditional coverage is undefined at zero selected mass. Selection is not automatically invalid: the error is reusing coverage without accounting for the selection rule.

View answer and explanation(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target)

average_only requires genuinely distinct coverages with weighted average≥target>minimum. posterior_confusion uses the explicit prior and observed sample to compute a different conditional quantity. ignored_selection retains each selected probability mass and recomputed conditional coverage, using undefined at zero mass. Selection is not automatically invalid; ignoring it is the error. invalid_procedure retains the actual validation error. The exact result, retaining the requested order, is (average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, Yes, Yes, Yes, No, average_coverage_can_mask_failure_of_uniform_target).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0100/)

Confidence-interval coverage in a finite model · qf-mod49-ci-interpretation-boundary · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations/validation-report.json)