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R0056-28554 · q-20261004-advance-20261005-r05-random-variable-0054
The nonempty finite sample space is S={0, 1, 2, 3}, with event family F=𝒫(S). The total function X:S→R has table {(0, -3), (1, -3), (2, 5), (3, 5)}. List the attained range X[S] in increasing order with each output value once.
G001 — The nonempty finite sample space is S={0, 1, 2, 3}, with event family F=𝒫(S). The total function X:S→R has table {(0, -3), (1, -3), (2, 5), (3, 5)}. List the attained range X[S] in increasing order with each output value once.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [qf-random-variable-range, rv_range]
After
derived = [all_attained_values_numeric_set]
Conditions: none
Use the declared scalar/set/Yes-No/fraction answer role;integer fractions retain/1.Do not add an undeclared domain or change original bilingual data,formulas or questions.
Rule: R56_source_answer_role_and_EXACT_family_interface · Uses: G001
Before
source roles = [[0, 1, 2, 3], powerset(S), [-3, -3, 5, 5]]
After
derived = [[[0, -3], [1, -3], [2, 5], [3, 5]]]
Conditions: none
Align each value with the ORIGINAL S slot,not independently sorted columns.The full powerset contains every preimage of this real-valued function,hence measurability.No invented uniform weights are needed for a value,range or event.
Rule: RV_full_powerset_measurability_ORIGINAL_outcome_value_alignment · Uses: G001, S001
Before
source roles = [[[0, -3], [1, -3], [2, 5], [3, 5]]]
After
derived = [[-3, 5], {-3, 5}]Conditions: none
Read EVERY outcome value,then deduplicate and sort numerically.The range consists of attained values,not outcomes or positive-mass support;zero-mass labels are not removed.
Rule: RV_range_ALL_attained_values_not_mass_support · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.S002 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.S001 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.{-3, 5}The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 03e9070ad541f21879ab7206e9da8aa4c394275a1331ceef4b319b2bae745504candidate record SHA-256: db7829c97307e9d31d5b2cec20a9551eabf452bc8b61b6716a807cbc9243276bsemantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759fLean: NOT_RUN · human review: NOT_PERFORMED