# Complete Fibre Pushforwards, Parameter Families and Nonclaim Markers

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

batch-20261014-advance-20261105-r06-sampling-distribution-foundations · 2026-10-14 · 100 questions

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

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

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



## 1. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/8, 2/8, 3/8, 2/8], [2/12, 3/12, 4/12, 3/12]], and one total parameter-independent statistic T=[0, 0, 1, 2] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/8], [1, 3/8], [2, 1/4]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/8], [1, 3/8], [2, 1/4]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0001/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 2. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/9, 2/9, 3/9, 3/9], [2/13, 3/13, 4/13, 4/13]], and one total parameter-independent statistic T=[0, 0, 2, 3] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/13], [2, 4/13], [3, 4/13]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/13], [2, 4/13], [3, 4/13]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0002/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 3. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/10, 2/10, 3/10, 4/10], [2/14, 3/14, 4/14, 5/14]], and one total parameter-independent statistic T=[0, 0, 3, 4] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/10], [3, 3/10], [4, 2/5]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/10], [3, 3/10], [4, 2/5]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0003/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 4. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/11, 2/11, 3/11, 5/11], [2/15, 3/15, 4/15, 6/15]], and one total parameter-independent statistic T=[0, 0, 4, 5] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 1/3], [4, 4/15], [5, 2/5]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 1/3], [4, 4/15], [5, 2/5]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0004/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 5. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/12, 2/12, 3/12, 6/12], [2/16, 3/16, 4/16, 7/16]], and one total parameter-independent statistic T=[0, 0, 5, 6] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 1/4], [5, 1/4], [6, 1/2]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 1/4], [5, 1/4], [6, 1/2]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0005/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 6. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/13, 2/13, 3/13, 7/13], [2/17, 3/17, 4/17, 8/17]], and one total parameter-independent statistic T=[0, 0, 6, 7] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/17], [6, 4/17], [7, 8/17]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/17], [6, 4/17], [7, 8/17]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0006/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 7. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/14, 2/14, 3/14, 8/14], [2/18, 3/18, 4/18, 9/18]], and one total parameter-independent statistic T=[0, 0, 7, 8] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/14], [7, 3/14], [8, 4/7]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/14], [7, 3/14], [8, 4/7]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0007/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 8. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/15, 2/15, 3/15, 9/15], [2/19, 3/19, 4/19, 10/19]], and one total parameter-independent statistic T=[0, 0, 8, 9] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/19], [8, 4/19], [9, 10/19]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/19], [8, 4/19], [9, 10/19]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0008/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 9. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/16, 2/16, 3/16, 10/16], [2/20, 3/20, 4/20, 11/20]], and one total parameter-independent statistic T=[0, 0, 9, 10] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/16], [9, 3/16], [10, 5/8]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/16], [9, 3/16], [10, 5/8]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0009/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 10. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/17, 2/17, 3/17, 11/17], [2/21, 3/21, 4/21, 12/21]], and one total parameter-independent statistic T=[0, 0, 10, 11] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/21], [10, 4/21], [11, 4/7]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/21], [10, 4/21], [11, 4/7]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0010/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 11. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/18, 2/18, 3/18, 12/18], [2/22, 3/22, 4/22, 13/22]], and one total parameter-independent statistic T=[0, 0, 11, 12] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 1/6], [11, 1/6], [12, 2/3]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 1/6], [11, 1/6], [12, 2/3]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0011/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 12. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/19, 2/19, 3/19, 13/19], [2/23, 3/23, 4/23, 14/23]], and one total parameter-independent statistic T=[0, 0, 12, 13] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/23], [12, 4/23], [13, 14/23]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/23], [12, 4/23], [13, 14/23]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0012/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 13. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/20, 2/20, 3/20, 14/20], [2/24, 3/24, 4/24, 15/24]], and one total parameter-independent statistic T=[0, 0, 13, 14] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/20], [13, 3/20], [14, 7/10]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/20], [13, 3/20], [14, 7/10]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0013/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 14. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/21, 2/21, 3/21, 15/21], [2/25, 3/25, 4/25, 16/25]], and one total parameter-independent statistic T=[0, 0, 14, 15] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 1/5], [14, 4/25], [15, 16/25]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 1/5], [14, 4/25], [15, 16/25]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0014/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 15. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/22, 2/22, 3/22, 16/22], [2/26, 3/26, 4/26, 17/26]], and one total parameter-independent statistic T=[0, 0, 15, 16] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/22], [15, 3/22], [16, 8/11]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/22], [15, 3/22], [16, 8/11]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0015/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 16. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/23, 2/23, 3/23, 17/23], [2/27, 3/27, 4/27, 18/27]], and one total parameter-independent statistic T=[0, 0, 16, 17] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/27], [16, 4/27], [17, 2/3]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/27], [16, 4/27], [17, 2/3]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0016/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 17. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/24, 2/24, 3/24, 18/24], [2/28, 3/28, 4/28, 19/28]], and one total parameter-independent statistic T=[0, 0, 17, 18] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 1/8], [17, 1/8], [18, 3/4]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 1/8], [17, 1/8], [18, 3/4]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0017/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 18. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/25, 2/25, 3/25, 19/25], [2/29, 3/29, 4/29, 20/29]], and one total parameter-independent statistic T=[0, 0, 18, 19] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/29], [18, 4/29], [19, 20/29]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/29], [18, 4/29], [19, 20/29]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0018/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 19. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/26, 2/26, 3/26, 20/26], [2/30, 3/30, 4/30, 21/30]], and one total parameter-independent statistic T=[0, 0, 19, 20] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/26], [19, 3/26], [20, 10/13]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/26], [19, 3/26], [20, 10/13]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0019/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 20. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/27, 2/27, 3/27, 21/27], [2/31, 3/31, 4/31, 22/31]], and one total parameter-independent statistic T=[0, 0, 20, 21] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/31], [20, 4/31], [21, 22/31]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/31], [20, 4/31], [21, 22/31]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0020/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 21. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/28, 2/28, 3/28, 22/28], [2/32, 3/32, 4/32, 23/32]], and one total parameter-independent statistic T=[0, 0, 21, 22] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/28], [21, 3/28], [22, 11/14]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/28], [21, 3/28], [22, 11/14]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0021/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 22. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/29, 2/29, 3/29, 23/29], [2/33, 3/33, 4/33, 24/33]], and one total parameter-independent statistic T=[0, 0, 22, 23] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 5/33], [22, 4/33], [23, 8/11]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 5/33], [22, 4/33], [23, 8/11]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0022/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 23. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/30, 2/30, 3/30, 24/30], [2/34, 3/34, 4/34, 25/34]], and one total parameter-independent statistic T=[0, 0, 23, 24] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 1/10], [23, 1/10], [24, 4/5]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 1/10], [23, 1/10], [24, 4/5]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0023/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 24. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/31, 2/31, 3/31, 25/31], [2/35, 3/35, 4/35, 26/35]], and one total parameter-independent statistic T=[0, 0, 24, 25] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(1, [[0, 1/7], [24, 4/35], [25, 26/35]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (1, [[0, 1/7], [24, 4/35], [25, 26/35]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0024/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 25. Sum Every Estimator Fibre under One Parameter Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/32, 2/32, 3/32, 26/32], [2/36, 3/36, 4/36, 27/36]], and one total parameter-independent statistic T=[0, 0, 25, 26] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0. Give (parameter, law, total_mass, model_qualified, certificate).

View answer and explanation(0, [[0, 3/32], [25, 3/32], [26, 13/16]], 1, Yes, pushforward_sum_over_estimator_fibres)

Return the increasing list of statistic-value/mass pairs, including zero entries, and its exact total mass. This pushforward is the sampling distribution conditional on the supplied parameter, not a posterior or a finite-data estimate. The exact result, retaining the requested order, is (0, [[0, 3/32], [25, 3/32], [26, 13/16]], 1, Yes, pushforward_sum_over_estimator_fibres).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0025/)

Sampling distribution · qf-mod36-sampling-pushforward-at-parameter · candidate





## 26. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/8, 2/8, 3/8, 2/8], [2/12, 3/12, 4/12, 3/12]], and one total parameter-independent statistic T=[0, 0, 1, 2] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 1, 2], [[0, [[0, 3/8], [1, 3/8], [2, 1/4]]], [1, [[0, 5/12], [1, 1/3], [2, 1/4]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 1, 2], [[0, [[0, 3/8], [1, 3/8], [2, 1/4]]], [1, [[0, 5/12], [1, 1/3], [2, 1/4]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0026/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 27. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/9, 2/9, 3/9, 3/9], [2/13, 3/13, 4/13, 4/13]], and one total parameter-independent statistic T=[0, 0, 2, 3] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 2, 3], [[0, [[0, 1/3], [2, 1/3], [3, 1/3]]], [1, [[0, 5/13], [2, 4/13], [3, 4/13]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 2, 3], [[0, [[0, 1/3], [2, 1/3], [3, 1/3]]], [1, [[0, 5/13], [2, 4/13], [3, 4/13]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0027/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 28. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/10, 2/10, 3/10, 4/10], [2/14, 3/14, 4/14, 5/14]], and one total parameter-independent statistic T=[0, 0, 3, 4] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 3, 4], [[0, [[0, 3/10], [3, 3/10], [4, 2/5]]], [1, [[0, 5/14], [3, 2/7], [4, 5/14]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 3, 4], [[0, [[0, 3/10], [3, 3/10], [4, 2/5]]], [1, [[0, 5/14], [3, 2/7], [4, 5/14]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0028/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 29. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/11, 2/11, 3/11, 5/11], [2/15, 3/15, 4/15, 6/15]], and one total parameter-independent statistic T=[0, 0, 4, 5] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 4, 5], [[0, [[0, 3/11], [4, 3/11], [5, 5/11]]], [1, [[0, 1/3], [4, 4/15], [5, 2/5]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 4, 5], [[0, [[0, 3/11], [4, 3/11], [5, 5/11]]], [1, [[0, 1/3], [4, 4/15], [5, 2/5]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0029/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 30. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/12, 2/12, 3/12, 6/12], [2/16, 3/16, 4/16, 7/16]], and one total parameter-independent statistic T=[0, 0, 5, 6] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 5, 6], [[0, [[0, 1/4], [5, 1/4], [6, 1/2]]], [1, [[0, 5/16], [5, 1/4], [6, 7/16]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 5, 6], [[0, [[0, 1/4], [5, 1/4], [6, 1/2]]], [1, [[0, 5/16], [5, 1/4], [6, 7/16]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0030/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 31. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/13, 2/13, 3/13, 7/13], [2/17, 3/17, 4/17, 8/17]], and one total parameter-independent statistic T=[0, 0, 6, 7] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 6, 7], [[0, [[0, 3/13], [6, 3/13], [7, 7/13]]], [1, [[0, 5/17], [6, 4/17], [7, 8/17]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 6, 7], [[0, [[0, 3/13], [6, 3/13], [7, 7/13]]], [1, [[0, 5/17], [6, 4/17], [7, 8/17]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0031/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 32. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/14, 2/14, 3/14, 8/14], [2/18, 3/18, 4/18, 9/18]], and one total parameter-independent statistic T=[0, 0, 7, 8] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 7, 8], [[0, [[0, 3/14], [7, 3/14], [8, 4/7]]], [1, [[0, 5/18], [7, 2/9], [8, 1/2]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 7, 8], [[0, [[0, 3/14], [7, 3/14], [8, 4/7]]], [1, [[0, 5/18], [7, 2/9], [8, 1/2]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0032/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 33. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/15, 2/15, 3/15, 9/15], [2/19, 3/19, 4/19, 10/19]], and one total parameter-independent statistic T=[0, 0, 8, 9] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 8, 9], [[0, [[0, 1/5], [8, 1/5], [9, 3/5]]], [1, [[0, 5/19], [8, 4/19], [9, 10/19]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 8, 9], [[0, [[0, 1/5], [8, 1/5], [9, 3/5]]], [1, [[0, 5/19], [8, 4/19], [9, 10/19]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0033/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 34. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/16, 2/16, 3/16, 10/16], [2/20, 3/20, 4/20, 11/20]], and one total parameter-independent statistic T=[0, 0, 9, 10] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 9, 10], [[0, [[0, 3/16], [9, 3/16], [10, 5/8]]], [1, [[0, 1/4], [9, 1/5], [10, 11/20]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 9, 10], [[0, [[0, 3/16], [9, 3/16], [10, 5/8]]], [1, [[0, 1/4], [9, 1/5], [10, 11/20]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0034/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 35. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/17, 2/17, 3/17, 11/17], [2/21, 3/21, 4/21, 12/21]], and one total parameter-independent statistic T=[0, 0, 10, 11] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 10, 11], [[0, [[0, 3/17], [10, 3/17], [11, 11/17]]], [1, [[0, 5/21], [10, 4/21], [11, 4/7]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 10, 11], [[0, [[0, 3/17], [10, 3/17], [11, 11/17]]], [1, [[0, 5/21], [10, 4/21], [11, 4/7]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0035/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 36. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/18, 2/18, 3/18, 12/18], [2/22, 3/22, 4/22, 13/22]], and one total parameter-independent statistic T=[0, 0, 11, 12] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 11, 12], [[0, [[0, 1/6], [11, 1/6], [12, 2/3]]], [1, [[0, 5/22], [11, 2/11], [12, 13/22]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 11, 12], [[0, [[0, 1/6], [11, 1/6], [12, 2/3]]], [1, [[0, 5/22], [11, 2/11], [12, 13/22]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0036/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 37. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/19, 2/19, 3/19, 13/19], [2/23, 3/23, 4/23, 14/23]], and one total parameter-independent statistic T=[0, 0, 12, 13] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 12, 13], [[0, [[0, 3/19], [12, 3/19], [13, 13/19]]], [1, [[0, 5/23], [12, 4/23], [13, 14/23]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 12, 13], [[0, [[0, 3/19], [12, 3/19], [13, 13/19]]], [1, [[0, 5/23], [12, 4/23], [13, 14/23]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0037/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 38. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/20, 2/20, 3/20, 14/20], [2/24, 3/24, 4/24, 15/24]], and one total parameter-independent statistic T=[0, 0, 13, 14] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 13, 14], [[0, [[0, 3/20], [13, 3/20], [14, 7/10]]], [1, [[0, 5/24], [13, 1/6], [14, 5/8]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 13, 14], [[0, [[0, 3/20], [13, 3/20], [14, 7/10]]], [1, [[0, 5/24], [13, 1/6], [14, 5/8]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0038/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 39. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/21, 2/21, 3/21, 15/21], [2/25, 3/25, 4/25, 16/25]], and one total parameter-independent statistic T=[0, 0, 14, 15] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 14, 15], [[0, [[0, 1/7], [14, 1/7], [15, 5/7]]], [1, [[0, 1/5], [14, 4/25], [15, 16/25]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 14, 15], [[0, [[0, 1/7], [14, 1/7], [15, 5/7]]], [1, [[0, 1/5], [14, 4/25], [15, 16/25]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0039/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 40. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/22, 2/22, 3/22, 16/22], [2/26, 3/26, 4/26, 17/26]], and one total parameter-independent statistic T=[0, 0, 15, 16] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 15, 16], [[0, [[0, 3/22], [15, 3/22], [16, 8/11]]], [1, [[0, 5/26], [15, 2/13], [16, 17/26]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 15, 16], [[0, [[0, 3/22], [15, 3/22], [16, 8/11]]], [1, [[0, 5/26], [15, 2/13], [16, 17/26]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0040/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 41. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/23, 2/23, 3/23, 17/23], [2/27, 3/27, 4/27, 18/27]], and one total parameter-independent statistic T=[0, 0, 16, 17] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 16, 17], [[0, [[0, 3/23], [16, 3/23], [17, 17/23]]], [1, [[0, 5/27], [16, 4/27], [17, 2/3]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 16, 17], [[0, [[0, 3/23], [16, 3/23], [17, 17/23]]], [1, [[0, 5/27], [16, 4/27], [17, 2/3]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0041/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 42. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/24, 2/24, 3/24, 18/24], [2/28, 3/28, 4/28, 19/28]], and one total parameter-independent statistic T=[0, 0, 17, 18] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 17, 18], [[0, [[0, 1/8], [17, 1/8], [18, 3/4]]], [1, [[0, 5/28], [17, 1/7], [18, 19/28]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 17, 18], [[0, [[0, 1/8], [17, 1/8], [18, 3/4]]], [1, [[0, 5/28], [17, 1/7], [18, 19/28]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0042/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 43. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/25, 2/25, 3/25, 19/25], [2/29, 3/29, 4/29, 20/29]], and one total parameter-independent statistic T=[0, 0, 18, 19] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 18, 19], [[0, [[0, 3/25], [18, 3/25], [19, 19/25]]], [1, [[0, 5/29], [18, 4/29], [19, 20/29]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 18, 19], [[0, [[0, 3/25], [18, 3/25], [19, 19/25]]], [1, [[0, 5/29], [18, 4/29], [19, 20/29]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0043/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 44. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/26, 2/26, 3/26, 20/26], [2/30, 3/30, 4/30, 21/30]], and one total parameter-independent statistic T=[0, 0, 19, 20] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 19, 20], [[0, [[0, 3/26], [19, 3/26], [20, 10/13]]], [1, [[0, 1/6], [19, 2/15], [20, 7/10]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 19, 20], [[0, [[0, 3/26], [19, 3/26], [20, 10/13]]], [1, [[0, 1/6], [19, 2/15], [20, 7/10]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0044/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 45. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/27, 2/27, 3/27, 21/27], [2/31, 3/31, 4/31, 22/31]], and one total parameter-independent statistic T=[0, 0, 20, 21] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 20, 21], [[0, [[0, 1/9], [20, 1/9], [21, 7/9]]], [1, [[0, 5/31], [20, 4/31], [21, 22/31]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 20, 21], [[0, [[0, 1/9], [20, 1/9], [21, 7/9]]], [1, [[0, 5/31], [20, 4/31], [21, 22/31]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0045/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 46. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/28, 2/28, 3/28, 22/28], [2/32, 3/32, 4/32, 23/32]], and one total parameter-independent statistic T=[0, 0, 21, 22] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 21, 22], [[0, [[0, 3/28], [21, 3/28], [22, 11/14]]], [1, [[0, 5/32], [21, 1/8], [22, 23/32]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 21, 22], [[0, [[0, 3/28], [21, 3/28], [22, 11/14]]], [1, [[0, 5/32], [21, 1/8], [22, 23/32]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0046/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 47. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/29, 2/29, 3/29, 23/29], [2/33, 3/33, 4/33, 24/33]], and one total parameter-independent statistic T=[0, 0, 22, 23] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 22, 23], [[0, [[0, 3/29], [22, 3/29], [23, 23/29]]], [1, [[0, 5/33], [22, 4/33], [23, 8/11]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 22, 23], [[0, [[0, 3/29], [22, 3/29], [23, 23/29]]], [1, [[0, 5/33], [22, 4/33], [23, 8/11]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0047/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 48. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/30, 2/30, 3/30, 24/30], [2/34, 3/34, 4/34, 25/34]], and one total parameter-independent statistic T=[0, 0, 23, 24] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 23, 24], [[0, [[0, 1/10], [23, 1/10], [24, 4/5]]], [1, [[0, 5/34], [23, 2/17], [24, 25/34]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 23, 24], [[0, [[0, 1/10], [23, 1/10], [24, 4/5]]], [1, [[0, 5/34], [23, 2/17], [24, 25/34]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0048/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 49. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/31, 2/31, 3/31, 25/31], [2/35, 3/35, 4/35, 26/35]], and one total parameter-independent statistic T=[0, 0, 24, 25] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 24, 25], [[0, [[0, 3/31], [24, 3/31], [25, 25/31]]], [1, [[0, 1/7], [24, 4/35], [25, 26/35]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 24, 25], [[0, [[0, 3/31], [24, 3/31], [25, 25/31]]], [1, [[0, 1/7], [24, 4/35], [25, 26/35]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0049/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 50. One Fixed Statistic Has a Family of Parameter-Indexed Laws

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/32, 2/32, 3/32, 26/32], [2/36, 3/36, 4/36, 27/36]], and one total parameter-independent statistic T=[0, 0, 25, 26] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, parameter_laws, model_qualified, certificate).

View answer and explanation([0, 0, 25, 26], [[0, [[0, 3/32], [25, 3/32], [26, 13/16]]], [1, [[0, 5/36], [25, 1/9], [26, 3/4]]]], Yes, one_theta_independent_total_statistic_family_of_laws)

Use the same statistic for every parameter row and report each pushforward in increasing parameter order. Do not average across parameters or add an unstated prior. The exact result, retaining the requested order, is ([0, 0, 25, 26], [[0, [[0, 3/32], [25, 3/32], [26, 13/16]]], [1, [[0, 5/36], [25, 1/9], [26, 3/4]]]], Yes, one_theta_independent_total_statistic_family_of_laws).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0050/)

Sampling distribution · qf-mod36-sampling-family-readback · candidate





## 51. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/8, 2/8, 3/8, 2/8], [2/12, 3/12, 4/12, 3/12]], and one total parameter-independent statistic T=[0, 0, 1, 2] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).

View answer and explanation(0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0051/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 52. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/9, 2/9, 3/9, 3/9], [2/13, 3/13, 4/13, 4/13]], and one total parameter-independent statistic T=[0, 0, 2, 3] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=1. Give (outcome, estimate, law, boundary).

View answer and explanation(1, 0, [[0, 5/13], [2, 4/13], [3, 4/13]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (1, 0, [[0, 5/13], [2, 4/13], [3, 4/13]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0052/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 53. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/10, 2/10, 3/10, 4/10], [2/14, 3/14, 4/14, 5/14]], and one total parameter-independent statistic T=[0, 0, 3, 4] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=2. Give (outcome, estimate, law, boundary).

View answer and explanation(2, 3, [[0, 3/10], [3, 3/10], [4, 2/5]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (2, 3, [[0, 3/10], [3, 3/10], [4, 2/5]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0053/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 54. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/11, 2/11, 3/11, 5/11], [2/15, 3/15, 4/15, 6/15]], and one total parameter-independent statistic T=[0, 0, 4, 5] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=3. Give (outcome, estimate, law, boundary).

View answer and explanation(3, 5, [[0, 1/3], [4, 4/15], [5, 2/5]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (3, 5, [[0, 1/3], [4, 4/15], [5, 2/5]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0054/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 55. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/12, 2/12, 3/12, 6/12], [2/16, 3/16, 4/16, 7/16]], and one total parameter-independent statistic T=[0, 0, 5, 6] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).

View answer and explanation(0, 0, [[0, 1/4], [5, 1/4], [6, 1/2]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 1/4], [5, 1/4], [6, 1/2]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0055/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 56. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/13, 2/13, 3/13, 7/13], [2/17, 3/17, 4/17, 8/17]], and one total parameter-independent statistic T=[0, 0, 6, 7] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=1. Give (outcome, estimate, law, boundary).

View answer and explanation(1, 0, [[0, 5/17], [6, 4/17], [7, 8/17]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (1, 0, [[0, 5/17], [6, 4/17], [7, 8/17]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0056/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 57. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/14, 2/14, 3/14, 8/14], [2/18, 3/18, 4/18, 9/18]], and one total parameter-independent statistic T=[0, 0, 7, 8] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=2. Give (outcome, estimate, law, boundary).

View answer and explanation(2, 7, [[0, 3/14], [7, 3/14], [8, 4/7]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (2, 7, [[0, 3/14], [7, 3/14], [8, 4/7]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0057/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 58. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/15, 2/15, 3/15, 9/15], [2/19, 3/19, 4/19, 10/19]], and one total parameter-independent statistic T=[0, 0, 8, 9] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=3. Give (outcome, estimate, law, boundary).

View answer and explanation(3, 9, [[0, 5/19], [8, 4/19], [9, 10/19]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (3, 9, [[0, 5/19], [8, 4/19], [9, 10/19]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0058/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 59. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/16, 2/16, 3/16, 10/16], [2/20, 3/20, 4/20, 11/20]], and one total parameter-independent statistic T=[0, 0, 9, 10] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).

View answer and explanation(0, 0, [[0, 3/16], [9, 3/16], [10, 5/8]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 3/16], [9, 3/16], [10, 5/8]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0059/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 60. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/17, 2/17, 3/17, 11/17], [2/21, 3/21, 4/21, 12/21]], and one total parameter-independent statistic T=[0, 0, 10, 11] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=1. Give (outcome, estimate, law, boundary).

View answer and explanation(1, 0, [[0, 5/21], [10, 4/21], [11, 4/7]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (1, 0, [[0, 5/21], [10, 4/21], [11, 4/7]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0060/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 61. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/18, 2/18, 3/18, 12/18], [2/22, 3/22, 4/22, 13/22]], and one total parameter-independent statistic T=[0, 0, 11, 12] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=2. Give (outcome, estimate, law, boundary).

View answer and explanation(2, 11, [[0, 1/6], [11, 1/6], [12, 2/3]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (2, 11, [[0, 1/6], [11, 1/6], [12, 2/3]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0061/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 62. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/19, 2/19, 3/19, 13/19], [2/23, 3/23, 4/23, 14/23]], and one total parameter-independent statistic T=[0, 0, 12, 13] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=3. Give (outcome, estimate, law, boundary).

View answer and explanation(3, 13, [[0, 5/23], [12, 4/23], [13, 14/23]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (3, 13, [[0, 5/23], [12, 4/23], [13, 14/23]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0062/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 63. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/20, 2/20, 3/20, 14/20], [2/24, 3/24, 4/24, 15/24]], and one total parameter-independent statistic T=[0, 0, 13, 14] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).

View answer and explanation(0, 0, [[0, 3/20], [13, 3/20], [14, 7/10]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 3/20], [13, 3/20], [14, 7/10]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0063/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 64. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/21, 2/21, 3/21, 15/21], [2/25, 3/25, 4/25, 16/25]], and one total parameter-independent statistic T=[0, 0, 14, 15] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=1. Give (outcome, estimate, law, boundary).

View answer and explanation(1, 0, [[0, 1/5], [14, 4/25], [15, 16/25]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (1, 0, [[0, 1/5], [14, 4/25], [15, 16/25]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0064/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 65. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/22, 2/22, 3/22, 16/22], [2/26, 3/26, 4/26, 17/26]], and one total parameter-independent statistic T=[0, 0, 15, 16] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=2. Give (outcome, estimate, law, boundary).

View answer and explanation(2, 15, [[0, 3/22], [15, 3/22], [16, 8/11]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (2, 15, [[0, 3/22], [15, 3/22], [16, 8/11]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0065/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 66. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/23, 2/23, 3/23, 17/23], [2/27, 3/27, 4/27, 18/27]], and one total parameter-independent statistic T=[0, 0, 16, 17] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=3. Give (outcome, estimate, law, boundary).

View answer and explanation(3, 17, [[0, 5/27], [16, 4/27], [17, 2/3]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (3, 17, [[0, 5/27], [16, 4/27], [17, 2/3]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0066/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 67. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/24, 2/24, 3/24, 18/24], [2/28, 3/28, 4/28, 19/28]], and one total parameter-independent statistic T=[0, 0, 17, 18] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).

View answer and explanation(0, 0, [[0, 1/8], [17, 1/8], [18, 3/4]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 1/8], [17, 1/8], [18, 3/4]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0067/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 68. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/25, 2/25, 3/25, 19/25], [2/29, 3/29, 4/29, 20/29]], and one total parameter-independent statistic T=[0, 0, 18, 19] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=1. Give (outcome, estimate, law, boundary).

View answer and explanation(1, 0, [[0, 5/29], [18, 4/29], [19, 20/29]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (1, 0, [[0, 5/29], [18, 4/29], [19, 20/29]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0068/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 69. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/26, 2/26, 3/26, 20/26], [2/30, 3/30, 4/30, 21/30]], and one total parameter-independent statistic T=[0, 0, 19, 20] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=2. Give (outcome, estimate, law, boundary).

View answer and explanation(2, 19, [[0, 3/26], [19, 3/26], [20, 10/13]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (2, 19, [[0, 3/26], [19, 3/26], [20, 10/13]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0069/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 70. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/27, 2/27, 3/27, 21/27], [2/31, 3/31, 4/31, 22/31]], and one total parameter-independent statistic T=[0, 0, 20, 21] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=3. Give (outcome, estimate, law, boundary).

View answer and explanation(3, 21, [[0, 5/31], [20, 4/31], [21, 22/31]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (3, 21, [[0, 5/31], [20, 4/31], [21, 22/31]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0070/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 71. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/28, 2/28, 3/28, 22/28], [2/32, 3/32, 4/32, 23/32]], and one total parameter-independent statistic T=[0, 0, 21, 22] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).

View answer and explanation(0, 0, [[0, 3/28], [21, 3/28], [22, 11/14]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 3/28], [21, 3/28], [22, 11/14]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0071/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 72. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/29, 2/29, 3/29, 23/29], [2/33, 3/33, 4/33, 24/33]], and one total parameter-independent statistic T=[0, 0, 22, 23] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=1. Give (outcome, estimate, law, boundary).

View answer and explanation(1, 0, [[0, 5/33], [22, 4/33], [23, 8/11]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (1, 0, [[0, 5/33], [22, 4/33], [23, 8/11]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0072/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 73. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/30, 2/30, 3/30, 24/30], [2/34, 3/34, 4/34, 25/34]], and one total parameter-independent statistic T=[0, 0, 23, 24] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=2. Give (outcome, estimate, law, boundary).

View answer and explanation(2, 23, [[0, 1/10], [23, 1/10], [24, 4/5]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (2, 23, [[0, 1/10], [23, 1/10], [24, 4/5]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0073/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 74. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/31, 2/31, 3/31, 25/31], [2/35, 3/35, 4/35, 26/35]], and one total parameter-independent statistic T=[0, 0, 24, 25] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=1; supplied outcome index=3. Give (outcome, estimate, law, boundary).

View answer and explanation(3, 25, [[0, 1/7], [24, 4/35], [25, 26/35]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (3, 25, [[0, 1/7], [24, 4/35], [25, 26/35]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0074/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 75. An Observed Estimate Is Not the Whole Sampling Law

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/32, 2/32, 3/32, 26/32], [2/36, 3/36, 4/36, 27/36]], and one total parameter-independent statistic T=[0, 0, 25, 26] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Selected parameter=0; supplied outcome index=0. Give (outcome, estimate, law, boundary).

View answer and explanation(0, 0, [[0, 3/32], [25, 3/32], [26, 13/16]], observed_estimate_is_not_sampling_distribution)

Read the statistic at the supplied outcome and retain the separate complete pushforward law at the selected parameter. One realized number does not replace that law or establish the unknown parameter. The exact result, retaining the requested order, is (0, 0, [[0, 3/32], [25, 3/32], [26, 13/16]], observed_estimate_is_not_sampling_distribution).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0075/)

Sampling distribution · qf-mod36-sampling-observed-estimate-boundary · candidate





## 76. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/8, 2/8, 3/8, 2/8], [2/12, 3/12, 4/12, 3/12]], and one total parameter-independent statistic T=[0, 0, 1, 2] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 1, 2], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 1, 2], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0076/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 77. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/9, 2/9, 3/9, 3/9], [2/13, 3/13, 4/13, 4/13]], and one total parameter-independent statistic T=[0, 0, 2, 3] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 2, 3], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 2, 3], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0077/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 78. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/10, 2/10, 3/10, 4/10], [2/14, 3/14, 4/14, 5/14]], and one total parameter-independent statistic T=[0, 0, 3, 4] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 3, 4], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 3, 4], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0078/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 79. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/11, 2/11, 3/11, 5/11], [2/15, 3/15, 4/15, 6/15]], and one total parameter-independent statistic T=[0, 0, 4, 5] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 4, 5], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 4, 5], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0079/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 80. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/12, 2/12, 3/12, 6/12], [2/16, 3/16, 4/16, 7/16]], and one total parameter-independent statistic T=[0, 0, 5, 6] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 5, 6], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 5, 6], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0080/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 81. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/13, 2/13, 3/13, 7/13], [2/17, 3/17, 4/17, 8/17]], and one total parameter-independent statistic T=[0, 0, 6, 7] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 6, 7], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 6, 7], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0081/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 82. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/14, 2/14, 3/14, 8/14], [2/18, 3/18, 4/18, 9/18]], and one total parameter-independent statistic T=[0, 0, 7, 8] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 7, 8], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 7, 8], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0082/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 83. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/15, 2/15, 3/15, 9/15], [2/19, 3/19, 4/19, 10/19]], and one total parameter-independent statistic T=[0, 0, 8, 9] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 8, 9], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 8, 9], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0083/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 84. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/16, 2/16, 3/16, 10/16], [2/20, 3/20, 4/20, 11/20]], and one total parameter-independent statistic T=[0, 0, 9, 10] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 9, 10], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 9, 10], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0084/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 85. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/17, 2/17, 3/17, 11/17], [2/21, 3/21, 4/21, 12/21]], and one total parameter-independent statistic T=[0, 0, 10, 11] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 10, 11], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 10, 11], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0085/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 86. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/18, 2/18, 3/18, 12/18], [2/22, 3/22, 4/22, 13/22]], and one total parameter-independent statistic T=[0, 0, 11, 12] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 11, 12], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 11, 12], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0086/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 87. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/19, 2/19, 3/19, 13/19], [2/23, 3/23, 4/23, 14/23]], and one total parameter-independent statistic T=[0, 0, 12, 13] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 12, 13], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 12, 13], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0087/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 88. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/20, 2/20, 3/20, 14/20], [2/24, 3/24, 4/24, 15/24]], and one total parameter-independent statistic T=[0, 0, 13, 14] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 13, 14], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 13, 14], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0088/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 89. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/21, 2/21, 3/21, 15/21], [2/25, 3/25, 4/25, 16/25]], and one total parameter-independent statistic T=[0, 0, 14, 15] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 14, 15], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 14, 15], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0089/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 90. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/22, 2/22, 3/22, 16/22], [2/26, 3/26, 4/26, 17/26]], and one total parameter-independent statistic T=[0, 0, 15, 16] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 15, 16], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 15, 16], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0090/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 91. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/23, 2/23, 3/23, 17/23], [2/27, 3/27, 4/27, 18/27]], and one total parameter-independent statistic T=[0, 0, 16, 17] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 16, 17], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 16, 17], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0091/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 92. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/24, 2/24, 3/24, 18/24], [2/28, 3/28, 4/28, 19/28]], and one total parameter-independent statistic T=[0, 0, 17, 18] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 17, 18], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 17, 18], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0092/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 93. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/25, 2/25, 3/25, 19/25], [2/29, 3/29, 4/29, 20/29]], and one total parameter-independent statistic T=[0, 0, 18, 19] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 18, 19], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 18, 19], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0093/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 94. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/26, 2/26, 3/26, 20/26], [2/30, 3/30, 4/30, 21/30]], and one total parameter-independent statistic T=[0, 0, 19, 20] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 19, 20], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 19, 20], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0094/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 95. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/27, 2/27, 3/27, 21/27], [2/31, 3/31, 4/31, 22/31]], and one total parameter-independent statistic T=[0, 0, 20, 21] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 20, 21], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 20, 21], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0095/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 96. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/28, 2/28, 3/28, 22/28], [2/32, 3/32, 4/32, 23/32]], and one total parameter-independent statistic T=[0, 0, 21, 22] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 21, 22], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 21, 22], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0096/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 97. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/29, 2/29, 3/29, 23/29], [2/33, 3/33, 4/33, 24/33]], and one total parameter-independent statistic T=[0, 0, 22, 23] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 22, 23], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 22, 23], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0097/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 98. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/30, 2/30, 3/30, 24/30], [2/34, 3/34, 4/34, 25/34]], and one total parameter-independent statistic T=[0, 0, 23, 24] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 23, 24], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 23, 24], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0098/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 99. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/31, 2/31, 3/31, 25/31], [2/35, 3/35, 4/35, 26/35]], and one total parameter-independent statistic T=[0, 0, 24, 25] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 24, 25], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 24, 25], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0099/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate





## 100. Withholding Statistical Claims Does Not Establish Their Negations

Use common outcomes=Fin(4)={0,…,3}, parameter indices=Fin(2)={0,…,1}, complete exact law rows=[[1/32, 2/32, 3/32, 26/32], [2/36, 3/36, 4/36, 27/36]], and one total parameter-independent statistic T=[0, 0, 25, 26] in outcome order. Every law is nonnegative and sums to1. For each parameter, add law masses over each T-fibre; list the distinct statistic values increasingly, retaining zero-mass fibres. A parameter law, a sampling law and an observed estimate are different objects; no prior or posterior is supplied. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).

The four No values withhold statistical, likelihood or posterior claims; they do not prove the corresponding properties false.

View answer and explanation([0, 0, 25, 26], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

Retain the four literal No nonclaim markers. The source boundary lists absent unbiasedness, low-variance, consistency, likelihood and posterior claims; it does not supply four named tests or prove any of those properties false. The exact result, retaining the requested order, is ([0, 0, 25, 26], No, No, No, No, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261105-r06-sampling-distribution-0100/)

Sampling distribution · qf-mod36-sampling-property-nonconclusion · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r06-sampling-distribution-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261014-advance-20261105-r06-sampling-distribution-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r06-sampling-distribution-foundations/validation-report.json)