Complete Law Tables, Likelihoods and Parameter-Observation Roles
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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-20261103-r04-parametric-statistical-model-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.
1. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/4, 1/4, 1/2], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/4, 1/4, 1/2], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
2. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/5, 1/5, 3/5], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/5, 1/5, 3/5], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
3. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/6, 1/6, 2/3], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/6, 1/6, 2/3], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
4. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/7, 1/7, 5/7], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/7, 1/7, 5/7], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
5. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/8, 1/8, 3/4], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/8, 1/8, 3/4], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
6. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/9, 1/9, 7/9], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/9, 1/9, 7/9], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
7. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/10, 1/10, 4/5], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/10, 1/10, 4/5], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
8. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/11, 1/11, 9/11], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/11, 1/11, 9/11], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
9. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/12, 1/12, 5/6], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/12, 1/12, 5/6], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
10. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/13, 1/13, 11/13], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/13, 1/13, 11/13], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
11. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/14, 1/14, 6/7], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/14, 1/14, 6/7], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
12. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/15, 1/15, 13/15], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/15, 1/15, 13/15], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
13. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/16, 1/16, 7/8], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/16, 1/16, 7/8], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
14. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/17, 1/17, 15/17], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/17, 1/17, 15/17], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
15. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/18, 1/18, 8/9], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/18, 1/18, 8/9], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
16. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/19, 1/19, 17/19], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/19, 1/19, 17/19], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
17. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/20, 1/20, 9/10], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/20, 1/20, 9/10], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
18. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/21, 1/21, 19/21], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/21, 1/21, 19/21], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
19. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/22, 1/22, 10/11], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/22, 1/22, 10/11], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
20. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/23, 1/23, 21/23], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/23, 1/23, 21/23], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
21. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/24, 1/24, 11/12], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/24, 1/24, 11/12], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
22. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/25, 1/25, 23/25], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/25, 1/25, 23/25], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
23. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/26, 1/26, 12/13], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/26, 1/26, 12/13], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
24. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/27, 1/27, 25/27], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/27, 1/27, 25/27], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
25. Every Parameter Row Must Qualify on the Same Sample Space
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. Give (parameter_count,outcome_count,law_rows,qualified?,common_sample_space). Each row is [parameter,probability_entries,row_sum,row_qualified?] in original parameter order.
View answer and explanation
(2, 3, [[0, [1/28, 1/28, 13/14], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space)
Audit every exact row sum and nonnegativity before conjoining qualification. Invalid candidate rows remain visible with their flags; calling an array a law table does not make it normalized. The exact result, retaining the requested order, is (2, 3, [[0, [1/28, 1/28, 13/14], 1, Yes], [1, [1/2, 1/3, 1/6], 1, Yes]], Yes, common_sample_space).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-qualification · candidate
26. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 0, 1/4, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 0, 1/4, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
27. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 1, 1/3, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 1, 1/3, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
28. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 2, 2/3, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 2, 2/3, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
29. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 0, 1/2, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 0, 1/2, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
30. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 1, 1/8, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 1, 1/8, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
31. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 2, 1/6, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 2, 1/6, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
32. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 0, 1/10, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 0, 1/10, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
33. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 1, 1/3, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 1, 1/3, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
34. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 2, 5/6, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 2, 5/6, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
35. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 0, 1/2, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 0, 1/2, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
36. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 1, 1/14, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 1, 1/14, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
37. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 2, 1/6, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 2, 1/6, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
38. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 0, 1/16, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 0, 1/16, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
39. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 1, 1/3, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 1, 1/3, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
40. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 2, 8/9, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 2, 8/9, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
41. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 0, 1/2, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 0, 1/2, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
42. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 1, 1/20, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 1, 1/20, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
43. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 2, 1/6, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 2, 1/6, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
44. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 0, 1/22, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 0, 1/22, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
45. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 1, 1/3, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 1, 1/3, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
46. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 2, 11/12, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 2, 11/12, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
47. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 0, 1/2, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 0, 1/2, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
48. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 1, 1/26, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 1, 1/26, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
49. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(1, 2, 1/6, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (1, 2, 1/6, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
50. Read One Parameter-Outcome Cell without Confusing Their Roles
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,probability,model_qualified?).
View answer and explanation
(0, 0, 1/28, Yes)
Select the row by parameter and column by observed outcome, then retain whole-table qualification separately. A raw cell from an invalid candidate table does not repair the model or become a posterior. The exact result, retaining the requested order, is (0, 0, 1/28, Yes).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-law-lookup · candidate
51. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/4], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/4], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
52. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/5], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/5], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
53. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 2/3], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 2/3], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
54. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/7], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/7], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
55. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/8], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/8], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
56. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 7/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 7/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
57. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/10], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/10], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
58. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/11], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/11], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
59. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 5/6], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 5/6], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
60. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/13], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/13], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
61. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/14], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/14], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
62. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 13/15], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 13/15], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
63. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/16], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/16], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
64. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/17], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/17], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
65. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 8/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 8/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
66. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/19], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/19], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
67. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/20], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/20], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
68. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 19/21], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 19/21], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
69. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/22], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/22], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
70. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/23], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/23], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
71. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 11/12], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 11/12], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
72. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/25], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/25], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
73. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=1. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(1, [[0, 1/26], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (1, [[0, 1/26], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
74. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=2. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(2, [[0, 25/27], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (2, [[0, 25/27], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
75. A Likelihood Varies the Parameter for One Fixed Observation
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. In the qualified model fix observed outcome=0. Give (outcome,likelihood_rows,likelihood_as_function_of_parameter_not_posterior), with rows [parameter,P_parameter(outcome)] in parameter order.
View answer and explanation
(0, [[0, 1/28], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)
Read that same outcome column across all parameter rows. These values need not sum to one over parameters and are not posterior probabilities; no parameter prior was supplied. The exact result, retaining the requested order, is (0, [[0, 1/28], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-likelihood · candidate
76. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 0, parameter_index, observed_outcome, 1/4, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 0, parameter_index, observed_outcome, 1/4, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
77. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
78. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 2, parameter_index, observed_outcome, 2/3, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 2, parameter_index, observed_outcome, 2/3, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
79. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
80. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 1, parameter_index, observed_outcome, 1/8, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 1, parameter_index, observed_outcome, 1/8, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
81. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
82. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 0, parameter_index, observed_outcome, 1/10, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 0, parameter_index, observed_outcome, 1/10, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
83. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
84. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 2, parameter_index, observed_outcome, 5/6, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 2, parameter_index, observed_outcome, 5/6, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
85. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
86. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 1, parameter_index, observed_outcome, 1/14, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 1, parameter_index, observed_outcome, 1/14, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
87. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
88. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 0, parameter_index, observed_outcome, 1/16, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 0, parameter_index, observed_outcome, 1/16, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
89. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
90. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 2, parameter_index, observed_outcome, 8/9, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 2, parameter_index, observed_outcome, 8/9, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
91. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
92. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 1, parameter_index, observed_outcome, 1/20, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 1, parameter_index, observed_outcome, 1/20, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
93. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
94. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 0, parameter_index, observed_outcome, 1/22, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 0, parameter_index, observed_outcome, 1/22, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
95. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 1, parameter_index, observed_outcome, 1/3, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
96. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 2, parameter_index, observed_outcome, 11/12, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 2, parameter_index, observed_outcome, 11/12, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
97. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 0, parameter_index, observed_outcome, 1/2, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
98. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=1. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 1, parameter_index, observed_outcome, 1/26, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 1, parameter_index, observed_outcome, 1/26, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
99. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=1, outcome=2. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (1, 2, parameter_index, observed_outcome, 1/6, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
100. Equal Numeric Indices Do Not Give Parameters and Observations the Same Role
Use parameter indices=Fin(2)={0,…,1} and one shared outcome space=Fin(3)={0,…,2}, with the complete parameter-by-outcome candidate law table=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]]. Every row must be nonnegative and sum exactly to 1 before the table qualifies as a statistical model. Keep parameter and observation roles distinct even when their numeric indices agree. A likelihood fixes the observed outcome and varies the parameter; no prior, posterior, identifiability or inferential optimality is implied. Rational computations are exact. parameter=0, outcome=0. Give (parameter,outcome,parameter_index,observed_outcome,law_value,same_role?,parameter_not_observation_and_likelihood_not_posterior).
View answer and explanation
(0, 0, parameter_index, observed_outcome, 1/28, No, parameter_not_observation_and_likelihood_not_posterior)
Read the cell under the stated parameter. The same_role No is about semantic roles, even when the numeric labels coincide. It does not classify a likelihood as a posterior or an observed outcome as an unknown parameter. The exact result, retaining the requested order, is (0, 0, parameter_index, observed_outcome, 1/28, No, parameter_not_observation_and_likelihood_not_posterior).
Reviewed step-by-step derivation
Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate
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