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