Explore related knowledge and questions →
← Question derivation index · Original question batch
R0056-28513 · q-20261004-advance-20261005-r05-random-variable-0013
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, -12), (1, -12), (2, 14), (3, 14)}. Find X(0), 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, -12), (1, -12), (2, 14), (3, 14)}. Find X(0), 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), [-12, -12, 14, 14]]
After
derived = [[[0, -12], [1, -12], [2, 14], [3, 14]]]
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, [[0, -12], [1, -12], [2, 14], [3, 14]]]
After
derived = [0, -12]
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.-12
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: 3447cd6bd2b0673ad4e9d85c48532164548d1882fe92b78605aee3719169c9afcandidate record SHA-256: 3f42876fd7de96fac5bffff18afd8f10b9daf55ce5b5197ed909ba26977dd74esemantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759fLean: NOT_RUN · human review: NOT_PERFORMED