Domain 07 · Mathematics Codex
Probability & Statistics
The mathematics of uncertainty — from card games to quantum mechanics to medical trials.
Scope
Probability theory, random variables, probability distributions, stochastic processes, Bayesian statistics, frequentist statistics, statistical inference, hypothesis testing, regression analysis.
Probability theory was initially motivated by gambling and games of chance. It became the foundation of statistical mechanics, quantum theory, and all of modern data science. The debate between Bayesian and frequentist interpretations of probability remains one of the live intellectual disputes in all of applied mathematics.
Entries in this domain
Build status: This domain is in active build. Live entries are marked below. All other entries are planned and pending — see build status for the full picture.
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Probability
Pending
A number between 0 and 1 measuring how likely an event is to occur — formally defined via measure theory.
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Random Variable
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A variable whose value is determined by a random process — the central object of probability theory.
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Normal Distribution
Pending
The bell-shaped probability distribution that describes the sum of many independent random variables — the Central Limit Theorem explains why it appears everywhere.