Outline of probability


Outline of probability

Probability is the likelihood or chance that something is the case or will happen. Probability theory is used extensively in statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

The following outline is provided as an overview and guide to the variety of topics included within the subject of probability.

Contents

Introduction

Basic probability

(Related topics: set theory, simple theorems in the algebra of sets)

Events

Elementary probability

Conditional probability

Independence

Probability theory

(Related topics: measure theory)

Measure-theoretic probability

Independence

Random variables

Discrete and continuous random variables

Expectation

Independence

Some common distributions

Some other distributions

Functions of random variables

  • Sums of random variables*
  • General functions of random variables*
  • Borel's paradox

Generating functions

(Related topics: integral transforms)

Common generating functions

Applications

Convergence of random variables

(Related topics: convergence)

Modes of convergence

Applications

Stochastic processes

Some common stochastic processes

Markov processes

Stochastic differential equations

Time series

Martingales

See also


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