{ "model": { "rank": 5343, "code": "thing-q176623", "model_id": "vr.tr.random-variable", "name": "random variable", "purpose": "Let an agent define random variables and their kinds, explain distributions, expectation and independence, relate the concept to statistics and modelling, and separate the concept from unrelated aliases in the registry entry.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q176623/", "tier": 2, "score": 68, "payload": { "layer": "wikidata", "aliases": [ "capsule toy", "complex random variable", "discrete random variable", "Hajek projection", "sample standard deviation", "confounding", "continuous random variable", "centred random variable", "standardized sample random variable", "centered variable", "Random closed set", "identically distributed", "moderation", "independent random variables", "real random variable", "hitting time" ], "aliasCount": 16, "merged": 16, "knownIn": 68, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q176623", "url": "https://www.wikidata.org/wiki/Q176623", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T22:30:46Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 3, "engine": "claude" }, "metaModel": { "id": "THING-Q176623", "registryId": "vr.tr.random-variable", "name": "random variable", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q176623/", "model": { "registry_id": "vr.tr.random-variable", "name": "random variable", "purpose": "Let an agent define random variables and their kinds, explain distributions, expectation and independence, relate the concept to statistics and modelling, and separate the concept from unrelated aliases in the registry entry.", "definition": "A variable whose value is determined by the outcome of a random experiment, formally a measurable function from a probability space to a set of values, usually real numbers, with a distribution describing the probabilities of its values; random variables are discrete, continuous or mixed, may be real, complex or vector valued, and are the basic objects of probability and statistics, with quantities such as the sample standard deviation being random variables computed from data.", "what_it_is_for": "Modelling uncertain quantities.", "affordances": [ "define the concept and kinds", "explain distributions and moments", "relate to statistics and modelling", "separate unrelated aliases" ], "distinguishing_features": [ "Measurable function on a probability space", "Distribution and moments", "Independence and dependence", "Foundation of statistics" ], "appearance": "Not a visible object; a symbol such as X with a distribution.", "visual_identification": [ "Value determined by a random outcome", "Discrete, continuous, real, complex or vector valued", "A parameter is fixed; a statistic is a random variable computed from a sample" ], "physical_properties": [], "families_and_kinds": [ "discrete random variables", "continuous random variables", "complex and vector-valued random variables", "statistics such as the sample mean and sample standard deviation", "projections and decompositions such as the Hajek projection", "random elements in general spaces" ], "related_models": [ { "relation": "is a kind of", "target": "random element", "why": "real-valued case" }, { "relation": "is a kind of", "target": "variable", "why": "in registry terms" }, { "relation": "has", "target": "probability distribution", "why": "its law" }, { "relation": "is studied by", "target": "probability theory", "why": "the discipline" } ], "identifiers": [], "standards_and_regulation": [ "ISO 3534 statistics vocabulary", "Notation conventions in probability texts" ], "failure_modes_and_hazards": [ "Confusing a random variable with its realisation or its distribution", "Assuming independence without justification", "Sense confusion with unrelated aliases such as capsule toys" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What a random variable is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and kinds.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a random variable, formally and intuitively, and what kinds exist?", "kind": "definition" }, { "text": "Is the question about a random variable, its distribution, a realisation or a parameter?", "kind": "boundary" } ] } ] }, { "id": "distribution", "name": "Distribution", "description": "Distributions.", "findings": [ { "id": "distribution-finding", "name": "Distribution", "description": "Distribution.", "questions": [ { "text": "How are distributions, densities and mass functions attached to random variables?", "kind": "definition" }, { "text": "Which entry fits probability distribution?", "kind": "action" } ] } ] } ] }, { "id": "compute", "name": "Compute", "description": "Moments and transformations.", "rationale": "Computation.", "layers": [ { "id": "moments", "name": "Moments", "description": "Expectation and variance.", "findings": [ { "id": "moments-finding", "name": "Moments", "description": "Moments.", "questions": [ { "text": "How are expectation, variance and other moments computed?", "kind": "action" }, { "text": "What are the values for the variable in question?", "kind": "measurement" } ] } ] }, { "id": "transform", "name": "Transform", "description": "Functions of random variables.", "findings": [ { "id": "transform-finding", "name": "Transform", "description": "Transform.", "questions": [ { "text": "How are sums, products and functions of random variables handled?", "kind": "action" }, { "text": "Which entry fits convolution of distributions?", "kind": "action" } ] } ] } ] }, { "id": "relations", "name": "Relations", "description": "Independence and dependence.", "rationale": "Theory.", "layers": [ { "id": "independence", "name": "Independence", "description": "Independence.", "findings": [ { "id": "independence-finding", "name": "Independence", "description": "Independence.", "questions": [ { "text": "What do independence, correlation and conditioning mean for random variables?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "limits", "name": "Limits", "description": "Limit theorems.", "findings": [ { "id": "limits-finding", "name": "Limits", "description": "Limits.", "questions": [ { "text": "What do the law of large numbers and central limit theorem say about sequences of random variables?", "kind": "provenance" }, { "text": "Which entry fits the central limit theorem?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Statistics and modelling.", "rationale": "Application.", "layers": [ { "id": "statistics", "name": "Statistics", "description": "Statistics as random variables.", "findings": [ { "id": "statistics-finding", "name": "Statistics", "description": "Statistics.", "questions": [ { "text": "How are sample statistics such as the standard deviation random variables, and why does it matter?", "kind": "provenance" }, { "text": "Which entry fits statistic?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How are random variables taught, and which misconceptions arise?", "kind": "provenance" }, { "text": "Which entry fits statistics education?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should discrete and continuous random variables be separate entries?", "How should probability references be linked?", "The registry entry has merged aliases for unrelated concepts such as capsule toys and confounding; should they be removed?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a random variable, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent define random variables and their kinds, explain distributions, expectation and independence, relate the concept to statistics and modelling, and separate the concept from unrelated aliases in the registry entry.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: capsule toy, complex random variable, discrete random variable, Hajek projection, sample standard deviation, confounding, continuous random variable, centred random variable, standardized sample random variable, centered variable, Random closed set, identically distributed.", "16 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 68 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a random variable, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "capsule toy", "complex random variable", "discrete random variable", "Hajek projection", "sample standard deviation", "confounding", "continuous random variable", "centred random variable", "standardized sample random variable", "centered variable", "Random closed set", "identically distributed" ] } ], "standing": "Described in 68 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 16 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one random variable from another, and a random variable from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a random variable sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a random variable from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a random variable passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a random variable between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a random variable, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a random variable is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What random variable is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of random variable are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is random variable operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of random variable and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of random variable?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as random variable?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a random variable came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a random variable and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a random variable is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a random variable, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a random variable, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a random variable is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }