Table of contents

1 General aspects 2 Foundations of probability theory 3 Random variables 4 Conditional probability 5 Probability distributions 6 Properties of probability distributions 7 Applied probability 8 Stochastic processes 9 Statistics 10 Applied statistics 11 Gambling 12 Financial mathematics 13 Physics 14 Genetics 15 Historical

General aspects

• Probability
• Randomness
• Uncertainty
• Statistical variability
• Observational error
• Average
• Probability interpretations
• Statistical regularity
• Central tendency
• Relative frequency
• Frequency probability
• Maximum likelihood
• Bayesian probability
• Principle of indifference
• Cox's theorem
• Eclectic probability
• Principle of maximum entropy
• Information entropy
• Urn problems
• Random number generator

• 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 probability
• Law of total expectation
• Law of total variance
• Almost surely
• Cox's theorem
• Edwin Thompson Jaynes
• Bayesianism
• Prior probability
• Posterior probability
• Borel's paradox
• Coherence (philosophical gambling strategy)

• Discrete random variable
  • Probability mass function
• Expected value
  • Jensen's inequality
• Variance
  • Standard deviation
• Moment (mathematics)
  • Moment about the mean
  • Standardized moment
    • Skewness
    • Kurtosis
    • Locality
  • Cumulant
• Multivariate random variable
• Independent identically-distributed random variables
• Statistical independence
  • Covariance
  • Covariance matrix
  • De Finetti's theorem
• Correlation
  • Uncorrelated
  • Correlation function
• Canonical correlation
• Convergence of random variables
• Markov's inequality
• Chebyshev's inequality
• Laws of large numbers
  • Asymptotic equipartition property
  • Typical set
• Martingale
  • Azuma's inequality

• Conditional expectation
• Bayes' theorem
• de Finetti's theorem

• Bose-Einstein statistics
• Bernoulli distribution
  • Bernoulli trial
• Beta distribution
• Binomial distribution
• Cauchy distribution
• Chi-square distribution
• Degenerate distribution
• Erlang distribution
• Exponential distribution
  • Exponential family
• F-distribution
• Fermi-Dirac statistics
• Fisher-Tippett distribution
• Gamma distribution
• Geometric distribution
• Maxwell-Boltzmann statistics
• Negative binomial distribution
• Normal distribution, also called the Gaussian distribution
  • Multivariate normal distribution
  • Matrix normal distribution
• Pareto distribution
• Poisson distribution
• Student's t-distribution
• Weibull distribution
• Wishart distribution
• Zeta distribution

• Central limit theorem
  • Illustration of the central limit theorem
  • Concrete illustration of the central limit theorem
• Characteristic function
• Location parameter
• Maxwell's theorem
• Moment-generating function
• Probability-generating function
• Vysochanskiï-Petunin inequality

• Empirical findings
  • Benford's law
  • Pareto principle
  • Zipf's law

• Random walk
• Markov chain
  • Examples of Markov chains
• Markov property
  • Hidden Markov model
• Bernoulli process
• Poisson process
• Time series analysis
  • Anomaly time series
• Brownian motion
• Wiener process
• Ito's lemma
• Branching process
• Gauss-Markov process
• Gaussian process
• Girsanov's theorem
• Queueing theory

• Statistical sample
  • Sampling (statistics)
  • Data point
  • Data set
  • Statistical population
  • Statistical phenomena
• 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

• Linear regression
• Statistical unit
• Statistical assembly
• Statistical model

• Game of chance
• Odds
• Betting
  • Spread betting
• Bookmaker
• Pari-mutuel gambling
• Gambler's ruin
• Poker probability
  • Pot odds
• The man who broke the bank at Monte Carlo

• Risk-neutral measure

• Probability amplitude

• Hardy-Weinberg principle