{"id":"random-variable","domain":"probability-statistics","type":"Concept","title":"Random Variable","slug":"random-variable","url":"/mathematics/probability-statistics/random-variable/","summary":"A function assigning numerical values to outcomes of a random process. Formally X:Omega->R, measurable. Basis for expected value, variance, distributions.","formal_definition":"X: (Omega,F,P) -> (R,B), a measurable function","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Feller, W. (1968/1971). An Introduction to Probability Theory and Its Applications. Vols 1-2, 3rd ed."},{"tier":1,"citation":"Billingsley, P. (1995). Probability and Measure. 3rd ed. Wiley."},{"tier":2,"citation":"Ross, S.M. (2014). A First Course in Probability. 9th ed. Pearson."}],"relationships":[{"type":"built_from","target":"probability","label":"Probability"},{"type":"leads_to","target":"normal-distribution","label":"Normal Distribution"},{"type":"uses","target":"function","label":"Function"},{"type":"uses","target":"integral","label":"Integral"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.7"}