random variable
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.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
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.
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.
It can be 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
What it looks like
Not a visible object; a symbol such as X with a distribution.
How it is recognised
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
Related models
is a kind of - real-valued case
is a kind of - in registry terms
has - its law
is studied by - the discipline
In practice
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
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
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Define What a random variable is.
Definition.
Definition
Definition and kinds.
Definition
Definition.
- What is a random variable, formally and intuitively, and what kinds exist? definition
- Is the question about a random variable, its distribution, a realisation or a parameter? boundary
Distribution
Distributions.
Distribution
Distribution.
- How are distributions, densities and mass functions attached to random variables? definition
- Which entry fits probability distribution? action
Compute Moments and transformations.
Computation.
Moments
Expectation and variance.
Moments
Moments.
- How are expectation, variance and other moments computed? action
- What are the values for the variable in question? measurement
Transform
Functions of random variables.
Transform
Transform.
- How are sums, products and functions of random variables handled? action
- Which entry fits convolution of distributions? action
Relations Independence and dependence.
Theory.
Independence
Independence.
Independence
Independence.
- What do independence, correlation and conditioning mean for random variables? provenance
- Which references are standard? provenance
Limits
Limit theorems.
Limits
Limits.
- What do the law of large numbers and central limit theorem say about sequences of random variables? provenance
- Which entry fits the central limit theorem? action
Apply Statistics and modelling.
Application.
Statistics
Statistics as random variables.
Statistics
Statistics.
- How are sample statistics such as the standard deviation random variables, and why does it matter? provenance
- Which entry fits statistic? action
Teach
Teaching.
Teach
Teaching.
- How are random variables taught, and which misconceptions arise? provenance
- Which entry fits statistics education? action
What the second pass must settle
- 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?