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R0056-28515 · q-20261004-advance-20261005-r05-random-variable-0015
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, -14), (1, -14), (2, 16), (3, -12)}. Find X(2), reading only the function value without assigning unspecified probabilities.
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, -14), (1, -14), (2, 16), (3, -12)}. Find X(2), reading only the function value without assigning unspecified probabilities.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-evaluation, rv_evaluate]
After
derived = [value_at_original_outcome]
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), [-14, -14, 16, -12]]
After
derived = [[[0, -14], [1, -14], [2, 16], [3, -12]]]
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 = [2, [[0, -14], [1, -14], [2, 16], [3, -12]]]
After
derived = [2, 16]
Conditions: none
First require s in S,then use its ORIGINAL slot to read X(s),not the same numeric index after sorting.
Rule: RV_evaluate_actual_member_and_raw_slot · 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.16
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: 90b84624e06cb74133dfec875c31743c40f5c7e8036d310b06e4ce34d9fc6e21candidate record SHA-256: 2644284074d0d3fa44e3f70f9952d9c128eb03343ce16b267a74506a0ad76428semantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759fLean: NOT_RUN · human review: NOT_PERFORMED