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One Total Statistic, Observed Estimates, Expectations and Nonclaim Markers

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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-20261014-advance-20261104-r04-statistical-estimator-foundations · 2026-10-14 · 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

1. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 1, 2], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 1, 2], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

2. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 2, 4], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 2, 4], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

3. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 3, 6], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 3, 6], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

4. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 4, 8], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 4, 8], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

5. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 5, 10], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 5, 10], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

6. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 6, 12], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 6, 12], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

7. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 7, 14], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 7, 14], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

8. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 8, 16], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 8, 16], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

9. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 9, 18], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 9, 18], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

10. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 10, 20], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 10, 20], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

11. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 11, 22], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 11, 22], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

12. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 12, 24], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 12, 24], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

13. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 13, 26], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 13, 26], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

14. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 14, 28], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 14, 28], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

15. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 15, 30], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 15, 30], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

16. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 16, 32], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 16, 32], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

17. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 17, 34], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 17, 34], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

18. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 18, 36], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 18, 36], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

19. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 19, 38], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 19, 38], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

20. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 20, 40], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 20, 40], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

21. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 21, 42], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 21, 42], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

22. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 22, 44], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 22, 44], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

23. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 23, 46], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 23, 46], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

24. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 24, 48], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 24, 48], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

25. A Total Statistic and a Qualified Model Are Separate Checks

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).

View answer and explanation

(2, 3, [0, 25, 50], Yes, Yes, single_total_statistic_independent_of_parameter)

Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 25, 50], Yes, Yes, single_total_statistic_independent_of_parameter).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-qualification · candidate

26. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

27. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 2, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 2, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

28. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 6, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 6, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

29. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

30. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 5, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 5, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

31. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 12, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 12, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

32. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

33. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 8, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 8, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

34. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 18, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 18, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

35. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

36. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 11, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 11, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

37. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 24, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 24, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

38. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

39. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 14, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 14, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

40. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 30, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 30, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

41. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

42. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 17, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 17, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

43. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 36, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 36, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

44. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

45. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 20, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 20, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

46. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 42, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 42, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

47. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

48. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).

View answer and explanation

(1, 23, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 23, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

49. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).

View answer and explanation

(2, 48, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 48, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

50. An Estimate Is the Observed Value of the Estimator Function

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).

View answer and explanation

(0, 0, estimate_value_not_estimator_function)

Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-observed-estimate · candidate

51. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 5/4, [0, 1, 2])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 5/4, [0, 1, 2]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

52. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 4/3, [0, 2, 4])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 4/3, [0, 2, 4]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

53. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 9/2, [0, 3, 6])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 9/2, [0, 3, 6]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

54. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 8/3, [0, 4, 8])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 8/3, [0, 4, 8]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

55. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 65/8, [0, 5, 10])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 65/8, [0, 5, 10]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

56. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 4, [0, 6, 12])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 4, [0, 6, 12]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

57. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 119/10, [0, 7, 14])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 119/10, [0, 7, 14]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

58. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 16/3, [0, 8, 16])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 16/3, [0, 8, 16]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

59. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 63/4, [0, 9, 18])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 63/4, [0, 9, 18]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

60. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 20/3, [0, 10, 20])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 20/3, [0, 10, 20]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

61. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 275/14, [0, 11, 22])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 275/14, [0, 11, 22]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

62. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 8, [0, 12, 24])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 8, [0, 12, 24]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

63. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 377/16, [0, 13, 26])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 377/16, [0, 13, 26]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

64. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 28/3, [0, 14, 28])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 28/3, [0, 14, 28]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

65. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 55/2, [0, 15, 30])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 55/2, [0, 15, 30]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

66. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 32/3, [0, 16, 32])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 32/3, [0, 16, 32]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

67. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 629/20, [0, 17, 34])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 629/20, [0, 17, 34]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

68. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 12, [0, 18, 36])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 12, [0, 18, 36]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

69. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 779/22, [0, 19, 38])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 779/22, [0, 19, 38]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

70. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 40/3, [0, 20, 40])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 40/3, [0, 20, 40]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

71. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 315/8, [0, 21, 42])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 315/8, [0, 21, 42]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

72. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 44/3, [0, 22, 44])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 44/3, [0, 22, 44]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

73. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 1127/26, [0, 23, 46])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 1127/26, [0, 23, 46]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

74. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).

View answer and explanation

(1, 16, [0, 24, 48])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 16, [0, 24, 48]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

75. Compute an Estimator Expectation under One Fixed Parameter Law

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).

View answer and explanation

(0, 1325/28, [0, 25, 50])

Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 1325/28, [0, 25, 50]).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-expectation-at-parameter · candidate

76. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 1, 2], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 1, 2], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

77. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 2, 4], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 2, 4], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

78. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 3, 6], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 3, 6], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

79. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 4, 8], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 4, 8], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

80. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 5, 10], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 5, 10], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

81. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 6, 12], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 6, 12], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

82. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 7, 14], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 7, 14], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

83. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 8, 16], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 8, 16], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

84. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 9, 18], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 9, 18], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

85. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 10, 20], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 10, 20], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

86. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 11, 22], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 11, 22], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

87. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 12, 24], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 12, 24], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

88. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 13, 26], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 13, 26], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

89. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 14, 28], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 14, 28], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

90. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 15, 30], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 15, 30], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

91. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 16, 32], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 16, 32], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

92. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 17, 34], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 17, 34], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

93. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 18, 36], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 18, 36], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

94. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 19, 38], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 19, 38], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

95. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 20, 40], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 20, 40], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

96. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 21, 42], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 21, 42], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

97. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 22, 44], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 22, 44], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

98. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 23, 46], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 23, 46], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

99. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 24, 48], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 24, 48], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

100. Withholding Statistical Claims Does Not Prove Their Negations

Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold property claims; they do not prove that the corresponding statistical properties are false.

View answer and explanation

([0, 25, 50], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)

These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 25, 50], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim).

Reviewed step-by-step derivation

Statistical estimator · qf-mod35-estimator-property-nonconclusion · candidate

Canonical question JSONL · English JSONL · Validation report