Complete Fibre Pushforwards, Parameter Families and Nonclaim Markers

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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Canonical question JSONL · English JSONL · Validation report