Probability is a measure of the likeliness that an event will occur. Probability is used to quantify an attitude of mind towards some proposition whose truth is not certain. The proposition of interest is usually of the form "A specific event will occur." The attitude of mind is of the form "How certain is it that the event will occur?" The certainty that is adopted can be described in terms of a numerical measure, and this number, between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty) is called the probability. 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.

Introduction

Basic probability

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

Events

Elementary probability

Meaning of probability

Calculating with probabilities

Independence

Probability theory

(Related topics: measure theory)

Measure-theoretic probability

Independence

Conditional probability

Random variables

Discrete and continuous random variables

Expectation

Independence

Some common distributions

Some other distributions

Functions of random variables

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