{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0001","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b7f04f324f3395ab107cbcf8f6bb9998cb469b53a697e9239145f1b39ae5e56","family_id":"qf-mod35-estimator-qualification","seed":202611044001,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,1,2]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 1, 2], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 1, 2], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0002","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7905910abe6109701333ab5478db5ea2141eb5b93e005a9388052f208893561b","family_id":"qf-mod35-estimator-qualification","seed":202611044002,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,2,4]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 2, 4], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 2, 4], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0003","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5838ef839fd59744faec1e60f3019b4e4719f63355a42d55ee991fe32ecd1c03","family_id":"qf-mod35-estimator-qualification","seed":202611044003,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,3,6]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 3, 6], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 3, 6], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0004","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64542cc95a61b39af8aef8ccc4cee5031c61019a0cf9bc3db5653e1a315a5661","family_id":"qf-mod35-estimator-qualification","seed":202611044004,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,4,8]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 4, 8], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 4, 8], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0005","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"319392712ed83589a88115cff06c7570afc5ab7173cf614a6378e06ab86cb900","family_id":"qf-mod35-estimator-qualification","seed":202611044005,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,5,10]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 5, 10], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 5, 10], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0006","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8e6b452ae5ea0fa8406cbb8427d05090995a939f939cec8269d62d1b51c43fd","family_id":"qf-mod35-estimator-qualification","seed":202611044006,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,6,12]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 6, 12], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 6, 12], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0007","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12718bc9c5ae7a2ecc77cf4f1c6155edbce095d8e541f9d68c33f9958ac8b910","family_id":"qf-mod35-estimator-qualification","seed":202611044007,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,7,14]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 7, 14], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 7, 14], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0008","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a6639b513a0eafcd630a603c6bb4dd209e61f7ba04639a1b20a94e58c07c771d","family_id":"qf-mod35-estimator-qualification","seed":202611044008,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 8, 16], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 8, 16], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0009","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a31cfcc2d423430fb412fabbc596a15ae93d17fd64b2fc568e8bb77db1fab0b","family_id":"qf-mod35-estimator-qualification","seed":202611044009,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,9,18]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 9, 18], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 9, 18], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0010","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"76b3cd1fd65ab09664f5e86eb92a5bc93d2d10d7cd4c38e1a593044bef4208ea","family_id":"qf-mod35-estimator-qualification","seed":202611044010,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,10,20]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 10, 20], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 10, 20], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0011","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"728d7129be14ffd0e15a45fbe317e4e1f9db0f6442c0e4af5000ea3ce3d3032b","family_id":"qf-mod35-estimator-qualification","seed":202611044011,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,11,22]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 11, 22], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 11, 22], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0012","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c19048790c501b946d7062b4d215195530462ecc1957fb1f921d222bcd1bb59b","family_id":"qf-mod35-estimator-qualification","seed":202611044012,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,12,24]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 12, 24], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 12, 24], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0013","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c8b6c2f130fb389248e2c1a6537b4705f3619f33ae3dd16bed3965e3451acee6","family_id":"qf-mod35-estimator-qualification","seed":202611044013,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,13,26]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 13, 26], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 13, 26], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0014","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c84469b84ab080b01dc79afc67b93ca2b0fac1ff7616947c7a0d1353aee8d888","family_id":"qf-mod35-estimator-qualification","seed":202611044014,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,14,28]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 14, 28], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 14, 28], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0015","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc5bc94e289d099b8f5a58dfe93bd2970d3576bb42c86250d98c7546240055f3","family_id":"qf-mod35-estimator-qualification","seed":202611044015,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,15,30]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 15, 30], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 15, 30], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0016","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"820193c849359cdb155dd0ca2025377583236ef5388544fc2ffcd9c2c3a7eaac","family_id":"qf-mod35-estimator-qualification","seed":202611044016,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,16,32]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 16, 32], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 16, 32], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0017","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec1839154479704367a58fa0ff9f0ec0501258768e3c414fe49f492d71469d41","family_id":"qf-mod35-estimator-qualification","seed":202611044017,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,17,34]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 17, 34], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 17, 34], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0018","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20cb3910e297dd7c7f70f863cf3ec447c9196266c52af69c96c192e996913c86","family_id":"qf-mod35-estimator-qualification","seed":202611044018,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,18,36]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 18, 36], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 18, 36], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0019","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9633893d6009a1a26669ea0f6da7d3ce3645adf8c1e0b700ac80730152a7260a","family_id":"qf-mod35-estimator-qualification","seed":202611044019,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,19,38]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 19, 38], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 19, 38], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0020","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"764e664048feca8f9ab61a4d7c824a26dbc02d105cb135a64a34cbd063ab7eae","family_id":"qf-mod35-estimator-qualification","seed":202611044020,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,20,40]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 20, 40], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 20, 40], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0021","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"937b4b62caa9895044fa498594caa955039204f8819b7d4927b2ce40a92a0dcb","family_id":"qf-mod35-estimator-qualification","seed":202611044021,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,21,42]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 21, 42], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 21, 42], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0022","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dae17b0b4e7f76f05ee26de81f2f1f4a355f683e441b9af6b0916b58cdeee454","family_id":"qf-mod35-estimator-qualification","seed":202611044022,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,22,44]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 22, 44], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 22, 44], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0023","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8f32f37c89baee57303fc44de9568357e1ea4c182c85357474620a1ba7f00293","family_id":"qf-mod35-estimator-qualification","seed":202611044023,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,23,46]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 23, 46], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 23, 46], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0024","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b4e389546ce80801b2c2113b76288478dade601f3fe98105b1f738d9d04fc0c","family_id":"qf-mod35-estimator-qualification","seed":202611044024,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,24,48]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 24, 48], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 24, 48], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0025","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64491734c173ad07c40c3dbd8a9305eb759d9ffabce5cc5068b5800160a5306d","family_id":"qf-mod35-estimator-qualification","seed":202611044025,"semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,25,50]}"},"fields":{"title":"A Total Statistic and a Qualified Model Are Separate Checks","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Give (parameter_count, outcome_count, statistic, model_qualified, statistic_total, certificate).","answer":{"kind":"expression","value":"(2, 3, [0, 25, 50], Yes, Yes, single_total_statistic_independent_of_parameter)","explanation":"Audit every law row and retain its combined model-qualification flag. The separate statistic-total flag records exactly one fixed statistic value per outcome, independent of the unknown parameter. A total array alone does not repair an invalid probability model. The exact result, retaining the requested order, is (2, 3, [0, 25, 50], Yes, Yes, single_total_statistic_independent_of_parameter)."},"skills":["A Total Statistic and a Qualified Model Are Separate Checks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0026","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b043cd78e2371e9467580d5f4c86ab57747b9729ccb507b42795b9b8944f4b2d","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044026,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,1,2]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0027","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"086659058ee20905c46617274dc262c9f6ace30a003da323946ab4ada4d25f25","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044027,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,2,4]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 2, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 2, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0028","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c29dc445ba563f9cc56aaf8d4ebfcad5e938dee0054ab4baec4747af663247a","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044028,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,3,6]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 6, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 6, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0029","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ff82e44248d4b8c7256ae990603dbeeb9654d7d47cdbf801c0b4f84ba601412","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044029,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,4,8]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0030","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"118a496fbd43db776e5897c427c9eda9eeaae969bbdc7f3ae86485df32a254d0","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044030,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,5,10]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 5, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 5, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0031","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c01f34af9cf0a2504ab07c99bd817500cd16d68b5143ac577f886b898ed6870","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044031,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,6,12]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 12, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 12, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0032","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c0589632c995bcaea81e0faa2366e5e5748a53760ffa694e05126ea5b4e9e2e1","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044032,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,7,14]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0033","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96ad563b4403b33f65ee633e9066b8e7b119b0c0d8d4e873fdfe4448c4526330","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044033,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 8, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 8, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0034","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f0bb64ca8c06e1088634f35fccc13fe114cd5fb2633bb851d3eb066ed53c474","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044034,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,9,18]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 18, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 18, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0035","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f0101112f44c7ee7a28942a9dd47fec9ccc45b33e6f3fcf5d15fe08eaf3d0968","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044035,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,10,20]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0036","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"779943592e8f4434e66085013835e70c804bee177b632cd4946dbca2b87d5975","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044036,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,11,22]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 11, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 11, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0037","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eacd2439a199e9e784cf66643a48c2ff8fd1da98dbbf58278ef1ca715a817c9b","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044037,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,12,24]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 24, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 24, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0038","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1af446aef6fe3159412f1aaf7b8e333a42156cad180f6d17a5d917219e0ac165","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044038,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,13,26]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0039","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03f82f12c12319ef2897b1d9eea1584f5290715afa2b2b5ed510ec1fb6af9f09","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044039,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,14,28]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 14, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 14, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0040","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a246621b8fc4a28d6f66e774755e929792e13c79c489c060d2da6d7fda40c47","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044040,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,15,30]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 30, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 30, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0041","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f7f8a6df5236cd34a0b8924c67c63838cf78cd37362ffa307d1ae5c469eff9fa","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044041,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,16,32]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0042","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e24fe8679708c9698d9c49b17fe3093ca1c41ba9a4b7c512fd1ba3ba67315cf1","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044042,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,17,34]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 17, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 17, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0043","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3f51b0c202fda5ab9fff18c2e62f387bb41d016b181eb7d7c13d4896a34607e6","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044043,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,18,36]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 36, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 36, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0044","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"278efbd3449d5ca2ae76723d70bf4b61ed19393ccd535896043216832aff8356","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044044,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,19,38]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0045","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3074929abe84bd79184fa54edbb14a9841095a059c1ad5899e455c786907c818","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044045,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,20,40]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 20, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 20, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0046","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e098e0e7501af1430757e75ef386317b25124c6a8b6f80b0e6676d83f142bc9","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044046,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,21,42]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 42, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 42, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0047","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"62e4cb49c8af95d51b2dd2ea6adcc6dc3b0181f0479bdcc10e8aae331166d9fe","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044047,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,22,44]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0048","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91dfc6807351aa6f1fa369bffa95adb9b32ef3c01e090bd9c2f8f26c3dfb0fb9","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044048,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,23,46]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=1. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(1, 23, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (1, 23, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0049","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec479f4234359d3e79a419443a063273f8a4dc915596e7935e3e4e68c1a65727","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044049,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,24,48]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=2. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(2, 48, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (2, 48, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0050","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37f228f7506f9d4a804999df2931235fd7f9909ddcfa00af978b8d98b1339cd9","family_id":"qf-mod35-estimator-observed-estimate","seed":202611044050,"semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,25,50]}"},"fields":{"title":"An Estimate Is the Observed Value of the Estimator Function","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. In the qualified model, observed outcome=0. Give (outcome, estimate, boundary).","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation":"Read T at that outcome only. The resulting number is an estimate, not a replacement for the full estimator function or the unknown parameter. The exact result, retaining the requested order, is (0, 0, estimate_value_not_estimator_function)."},"skills":["An Estimate Is the Observed Value of the Estimator Function"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0051","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d20fe367d9eaf0cd88e351cd116e131094c56ad13a224a216ddb8603b1b2be9","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044051,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,1,2]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 5/4, [0, 1, 2])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 5/4, [0, 1, 2])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0052","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a86db2d8961eb4dcec8f482a89275acb3d8cf94e9244f4d329862a450c45685","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044052,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,2,4]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 4/3, [0, 2, 4])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 4/3, [0, 2, 4])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0053","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ea91411be34b6d1c43c2ccc047ade8a98a505a14b8bf8197169adcc28fb170e","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044053,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,3,6]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 9/2, [0, 3, 6])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 9/2, [0, 3, 6])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0054","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"97de3ef4606f58421757a2d1fb89dc9ea51b4c7ac7f516fc7e0a4595ff2507f9","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044054,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,4,8]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 8/3, [0, 4, 8])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 8/3, [0, 4, 8])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0055","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e1954692a0c44a7ea1808726eb8069082f3ef374194b5d9c8b957444280c24c0","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044055,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,5,10]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 65/8, [0, 5, 10])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 65/8, [0, 5, 10])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0056","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5274e8666141c95738beb50f7d4f5069199ccfd11023dc46c7f7fef6bded8800","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044056,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,6,12]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 4, [0, 6, 12])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 4, [0, 6, 12])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0057","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c141ce11f7fde928472cf717e7319fe68fa8edc09c42ad16327c3df571a3176","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044057,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,7,14]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 119/10, [0, 7, 14])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 119/10, [0, 7, 14])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0058","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df8a2eadc1e07b76925e48bce75dfdcdeb98337aa224006679c311604b6e65fb","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044058,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,8,16]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 16/3, [0, 8, 16])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 16/3, [0, 8, 16])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0059","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c92611c659d66d91833d25bad6dc8884f5c5ab50b1bb87fb7ee46aeb91c5275","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044059,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,9,18]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 63/4, [0, 9, 18])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 63/4, [0, 9, 18])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0060","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"af86d4ef9f8ddc22b5ca44fcfdc587a3d8834361003bb97cb45eed213363b891","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044060,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,10,20]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 20/3, [0, 10, 20])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 20/3, [0, 10, 20])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0061","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"881520e641ac0174bc15784bed6fc0c56b16a107d64ddfa1366e05a0ee0334c3","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044061,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,11,22]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 275/14, [0, 11, 22])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 275/14, [0, 11, 22])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0062","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c800596228de329cd0a74972a79632159caeda5bf2cb7975ddbf7bd1892203f","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044062,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,12,24]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 8, [0, 12, 24])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 8, [0, 12, 24])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0063","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31b7de621e9cd17c136afb95eacd32fd65129435ae8bc9a9b1e4159d2947cc7d","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044063,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,13,26]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 377/16, [0, 13, 26])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 377/16, [0, 13, 26])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0064","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9b8f94a70848026706a6e2b811f47e35ab8e2683172451a056835907774077c","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044064,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,14,28]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 28/3, [0, 14, 28])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 28/3, [0, 14, 28])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0065","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7058d9bd32478ba238f257d8bea924f94264644afaa8cc32ee9f0a0cb3e3e591","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044065,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,15,30]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 55/2, [0, 15, 30])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 55/2, [0, 15, 30])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0066","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"794cf4bb15159c6574d3b66e428bd09ee1a0458f96184fe59578d825958ff8b0","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044066,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,16,32]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 32/3, [0, 16, 32])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 32/3, [0, 16, 32])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0067","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"517c0ebfeae0a317deb1c7cd95240fbb6bb8038732b6acea92d712f13d1e5351","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044067,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,17,34]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 629/20, [0, 17, 34])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 629/20, [0, 17, 34])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0068","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4dfb146ff34c410696980e1b20286240e2ba2bb6f34b935291aa68f0f9d9f6e","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044068,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,18,36]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 12, [0, 18, 36])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 12, [0, 18, 36])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0069","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52a4bd4ad132feefde2709a8929bb19f2b6f749a043bc11d9707aa4288444a56","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044069,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,19,38]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 779/22, [0, 19, 38])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 779/22, [0, 19, 38])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0070","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b2d47891882d81d8cf61398c461ef1aa2f135d1e8764f1f0fe89034e0d10beae","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044070,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,20,40]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 40/3, [0, 20, 40])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 40/3, [0, 20, 40])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0071","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"633da7959e51fcc258e4ae310ff39b4fd9d16d962dd704935c60a330df3e34ed","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044071,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,21,42]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 315/8, [0, 21, 42])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 315/8, [0, 21, 42])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0072","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"082563f25eba8ae8cf475b5f6a0b6b103c7cb4ad979da0f57adf1e883dc5591c","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044072,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,22,44]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 44/3, [0, 22, 44])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 44/3, [0, 22, 44])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0073","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa9d5ddc1802c70102389c6c8fce20c201b9989d9f790b284f898630e6fd7623","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044073,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,23,46]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 1127/26, [0, 23, 46])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 1127/26, [0, 23, 46])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0074","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f7b7da76fdd577247518c130b49534a70282f01cddcdaf9a4ef87298c2bb9f0","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044074,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,24,48]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=1. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(1, 16, [0, 24, 48])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (1, 16, [0, 24, 48])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0075","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52d347d3f94025a82323ec9320ea566a9c2480ffa53a501c6157c7bb6543f3cc","family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044075,"semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,25,50]}"},"fields":{"title":"Compute an Estimator Expectation under One Fixed Parameter Law","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Qualified-model parameter index=0. Give (parameter, expectation, statistic).","answer":{"kind":"expression","value":"(0, 1325/28, [0, 25, 50])","explanation":"Weight the same statistic values by the selected complete law and sum exactly. This expectation does not establish unbiasedness without a declared estimand, or a posterior without a prior. The exact result, retaining the requested order, is (0, 1325/28, [0, 25, 50])."},"skills":["Compute an Estimator Expectation under One Fixed Parameter Law"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0076","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11980bd68c60cff1194f0fd5ad8a01653ca5c1159eb80d9e0f2db94ed3e86044","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044076,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,1,2]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/4, 1/4, 2/4], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 1, 2] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 1, 2], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 1, 2], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0077","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a496464abd2ff5c88e61f3512765aa588f8798956675d08c54756d80a5137aef","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044077,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,2,4]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/5, 1/5, 3/5], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 2, 4] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 2, 4], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 2, 4], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0078","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e99192400eb5d0dc654947eb2ce5405f022aff40f655058719025b4a650ab871","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044078,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,3,6]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/6, 1/6, 4/6], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 3, 6] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 3, 6], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 3, 6], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0079","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53714c40ff7ea0fe0953dbe5cc75ff09cffbba9c2e97d3a43b8ec544785cb36e","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044079,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,4,8]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/7, 1/7, 5/7], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 4, 8] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 4, 8], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 4, 8], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0080","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d36f1a574ae59d95dc34bb71433c37852414a44418fbef8d5d011daa5c004c52","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044080,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,5,10]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/8, 1/8, 6/8], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 5, 10] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 5, 10], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 5, 10], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0081","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"402df9eb16eb6891e7b99d4032e91d42972c6bcb8570e85b6a293a961b648b79","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044081,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,6,12]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/9, 1/9, 7/9], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 6, 12] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 6, 12], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 6, 12], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0082","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"030aed7acd9e99ebbdc65d5e8330f5b920c2a61aef0e4730f37d3680f9ef64aa","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044082,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,7,14]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/10, 1/10, 8/10], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 7, 14] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 7, 14], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 7, 14], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0083","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c640791920c9482f976f0b0a048c20673f2e1147275cdd0344237df927eb818","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044083,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/11, 1/11, 9/11], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 8, 16] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 8, 16], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 8, 16], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0084","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4a0d12fdd4b3a803fdeafc41686fba488dcbf50cf188d46e70acb09e53e5ccc","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044084,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,9,18]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/12, 1/12, 10/12], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 9, 18] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 9, 18], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 9, 18], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0085","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"936ad3f8398b98213093277c73f224da3141b6b7783d37fb4e85359d6de57c0a","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044085,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,10,20]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/13, 1/13, 11/13], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 10, 20] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 10, 20], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 10, 20], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0086","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"947edea37877fbf75ab9078916db736c481a6db1cf249621bb285dfec756fe1f","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044086,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,11,22]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/14, 1/14, 12/14], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 11, 22] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 11, 22], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 11, 22], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0087","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75b2f6e8dcbd62c206ec7d8a5871eadf99e4b6eaf96d989725754c0976b8e7b6","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044087,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,12,24]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/15, 1/15, 13/15], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 12, 24] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 12, 24], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 12, 24], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0088","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bef07cde44af79ca1e97ebe0f18ba4edbbae1b52172e108c2aae9390e80fd232","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044088,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,13,26]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/16, 1/16, 14/16], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 13, 26] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 13, 26], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 13, 26], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0089","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2dad66e3e64c191eb91c8d83a23a287ea58061e95bc1c974616f732a4f7a1bac","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044089,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,14,28]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/17, 1/17, 15/17], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 14, 28] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 14, 28], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 14, 28], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0090","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f5dcd2b72ac447fbe45f99cb7b8e8a5374c59b055b2190513425cd041243080","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044090,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,15,30]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/18, 1/18, 16/18], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 15, 30] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 15, 30], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 15, 30], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0091","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb61f00cd853da16f0a79fa349fc26a55dc351ac3c26bceec6cb4f810c65a721","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044091,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,16,32]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/19, 1/19, 17/19], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 16, 32] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 16, 32], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 16, 32], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0092","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d97dc2ed79e83685eaf9f80e90a8d1307dc5edb6bf48da16101c0cc9c73b0734","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044092,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,17,34]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/20, 1/20, 18/20], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 17, 34] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 17, 34], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 17, 34], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0093","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"af26688e056e4a1f496d207ec679d00f13269263be9f31b41af3088dc12dfe1b","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044093,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,18,36]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/21, 1/21, 19/21], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 18, 36] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 18, 36], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 18, 36], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0094","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1b429d43d50a0e3d1e0d2236b23316037267db6001d789a9fa77709ade82616","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044094,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,19,38]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/22, 1/22, 20/22], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 19, 38] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 19, 38], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 19, 38], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0095","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0bfb45dd30124b5bac5ff1267be236fe75ac43973cdd464ad3440ad27735e9d2","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044095,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,20,40]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/23, 1/23, 21/23], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 20, 40] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 20, 40], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 20, 40], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0096","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac712613661705a7535f3ab288567249820fb19c4c94185e8d739014332c5dc4","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044096,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,21,42]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/24, 1/24, 22/24], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 21, 42] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 21, 42], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 21, 42], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0097","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0206da86b755815700e1dbc1ca6b45fa9d41aa59686dd6891c54fc601077b4f8","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044097,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,22,44]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/25, 1/25, 23/25], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 22, 44] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 22, 44], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 22, 44], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0098","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9bb2faffc67cd0345404756a84695871477592dacd3576e6f4ae4c1d54ede69d","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044098,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,23,46]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/26, 1/26, 24/26], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 23, 46] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 23, 46], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 23, 46], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0099","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d07ee134707802c31fd3db0ffb13d1db578caced383afbabf9288e8a6685be92","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044099,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,24,48]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/27, 1/27, 25/27], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 24, 48] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 24, 48], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 24, 48], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261104-r04-statistical-estimator-0100","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23800a525079d08c7ea37cb4b4a6da2c1b34cff504770ed5955faff1e7740d6a","family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044100,"semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,25,50]}"},"fields":{"title":"Withholding Statistical Claims Does Not Prove Their Negations","stem":"Use one common finite model with parameter indices=Fin(2)={0,…,1}, outcomes=Fin(3)={0,…,2}, complete candidate laws=[[1/28, 1/28, 26/28], [1/2, 1/3, 1/6]], and the single total statistic T=[0, 25, 50] in outcome order. Each law must be nonnegative and sum to 1 before model qualification. T depends on the observation, not the unknown parameter. An observed value is an estimate, while T is the estimator function; no prior or posterior is supplied. Retain four literal No claim markers in the declared tuple. Give (statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary).","answer":{"kind":"expression","value":"([0, 25, 50], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation":"These are nonconclusion markers, not four statistical tests or four proved failures. No unbiasedness, consistency, sufficiency, identifiability, posterior or full sampling-distribution conclusion is supplied by this definition-level audit. The exact result, retaining the requested order, is ([0, 25, 50], No, No, No, No, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)."},"skills":["Withholding Statistical Claims Does Not Prove Their Negations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}