# 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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0001/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0002/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0003/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0004/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0005/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0006/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0007/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0008/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0009/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0010/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0011/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0012/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0013/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0014/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0015/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0016/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0017/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0018/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0019/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0020/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0021/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0022/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0023/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0024/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0025/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0026/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0027/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0028/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0029/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0030/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0031/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0032/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0033/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0034/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0035/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0036/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0037/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0038/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0039/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0040/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0041/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0042/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0043/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0044/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0045/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0046/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0047/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0048/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0049/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0050/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0051/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0052/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0053/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0054/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0055/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0056/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0057/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0058/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0059/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0060/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0061/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0062/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0063/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0064/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0065/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0066/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0067/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0068/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0069/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0070/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0071/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0072/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0073/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0074/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0075/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0076/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0077/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0078/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0079/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0080/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0081/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0082/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0083/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0084/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0085/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0086/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0087/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0088/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0089/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0090/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0091/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0092/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0093/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0094/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0095/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0096/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0097/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0098/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0099/)

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](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261103-r04-parametric-statistical-model-0100/)

Parametric statistical model · qf-mod34-statmodel-parameter-observation-boundary · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations/validation-report.json)