# List of probability topics

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## Overview

This is a **list of probability topics**, by WikiDoc page.

It overlaps with the (alphabetical) list of statistical topics. There are also the list of probabilists and list of statisticians.

## General aspects

- Probability
- Randomness, Pseudorandomness, Quasirandom
- Randomization, hardware random number generator
- Random number generator
- Random sequence
- Coin flipping/tossing; checking if a coin is biased
- Uncertainty
- Statistical dispersion
- Observational error
- Average
- Probability interpretations
- Markovian
- Statistical regularity
- Central tendency
- Bean machine
- Relative frequency
- Frequency probability
- Maximum likelihood
- Bayesian probability
- Principle of indifference
- Cox's theorem
- Principle of maximum entropy
- Information entropy
- Urn problems
- Extractor
- Aleatoric, aleatoric music
- Free probability
- Exotic probability
- Schrödinger method
- Kolmogorov's zero-one law
- Hewitt-Savage zero-one law

## Foundations of probability theory

- Probability theory
- Sample space
- Probability space
- Probability axioms
- Normalizing constant
- Event (probability theory)
- Elementary event
- Mutually exclusive
- Boole's inequality
- Probability density function
- Cumulative distribution function
- Law of total cumulance
- Law of total expectation
- Law of total probability
- Law of total variance
- Almost surely
- Cox's theorem
- Edwin Thompson Jaynes
- Bayesianism
- Prior probability
- Posterior probability
- Borel's paradox
- Bertrand's paradox
- Coherence (philosophical gambling strategy)
- Dutch book
- Algebra of random variables
- Belief propagation
- Transferable belief model
- Dempster-Shafer theory
- Possibility theory

## Random variables

- Discrete random variable
- Constant random variable
- Expected value
- Variance
- Moment (mathematics)
- Multivariate random variable
- Independent identically-distributed random variables
- Statistical independence
- Correlation
- Canonical correlation
- Convergence of random variables
- Markov's inequality
- Chebyshev's inequality
- Chernoff's inequality
- Laws of large numbers
- Random field
- Borel-Cantelli lemma
- Wick product

## Conditional probability

- Conditional expectation
- Conditional distribution
- Marginal distribution
- Bayes' theorem
- de Finetti's theorem
- Rule of succession
- Conditional independence

## Probability distributions

- Bose-Einstein statistics
- Bernoulli distribution
- Beta distribution
- Binomial distribution
- Cantor distribution
- Cauchy distribution
- Chi-square distribution
- Continuity correction
- Copula (statistics)
- Degenerate distribution
- Dirichlet distribution
- Erlang distribution
- Exponential distribution
- F-distribution
- Fermi-Dirac statistics
- Fisher-Tippett distribution
- Gamma distribution
- Geometric distribution
- Graphical model
- Lévy distribution
- Levy skew alpha-stable distribution
- Maxwell-Boltzmann statistics
- Moment (mathematics)
- Multinomial distribution
- Negative binomial distribution
- Normal distribution, also called the Gaussian distribution
- Memorylessness
- Pareto distribution
- Phase-type distribution
- Poisson distribution
- Prior probability distribution
- stable distributions
- Student's t-distribution
- Total variation distance
- Triangular distribution
- Weibull distribution
- Wigner semicircle distribution
- Wishart distribution
- Zeta distribution
- Infinitely divisible distribution
- Indecomposable distribution

## Properties of probability distributions

- Central limit theorem
- Characteristic function (probability theory)
- Edgeworth series
- Helly-Bray theorem
- Limit theorem
- Location parameter
- Maxwell's theorem
- Moment-generating function
- Probability-generating function
- Vysochanskiï-Petunin inequality
- Mutual information
- Kullback-Leibler divergence
- Normally distributed and uncorrelated does not imply independent
- Le Cam's theorem
- Stability (probability)

## Applied probability

*Empirical findings*

## Stochastic processes

- Adapted process
- Bernoulli process
- Branching process
- Brownian motion
- Chapman-Kolmogorov equation
- Chinese restaurant process
- Coupling (probability)
- Ergodic theory
- Galton-Watson process
- Gauss-Markov process
- Gaussian process
- Girsanov's theorem
- Itô's lemma
- Law of the iterated logarithm
- Lévy flight
- Lévy process
- Loop-erased random walk
- Markov chain
- Markov property
- Martingale
- Poisson process
- Population process
- Process with independent increments
- Progressively measurable process
- Queueing theory
- Random walk
- Random walk Monte Carlo
- Skorokhod's embedding theorem
- Stationary process
- Stochastic calculus
- Time series analysis
- Wiener process

## Geometric probability

## Statistics

- List of statistical topics
- Statistical sample
- Statistical theory
- Statistical inference
- Null hypothesis
- Confidence interval
- Margin of error
- Interval estimation
- point estimation
- Estimator
- Bias (statistics)
- Gauss-Markov theorem
- Likelihood-ratio test
- Multivariate statistics
- Analysis of variance
- ANCOVA
- Bayesian inference

## Applied statistics

## Algorithmics

- Probable prime
- Probabilistic algorithm = Randomised algorithm
- Monte Carlo method
- Las Vegas algorithm
- Probabilistic Turing machine
- Stochastic programming
- Probabilistically checkable proof
- Box-Muller transform
- Metropolis algorithm
- Gibbs sampling
- Inverse transform sampling method

## Physics

- Probability amplitude
- Statistical physics
- Boltzmann factor
- Feynman-Kac formula
- Fluctuation theorem
- Information entropy
- Vacuum expectation value
- Brownian ratchet
- Cosmic variance

## Percolation theory

## Genetics

## Historical