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

edit

Basic probability

edit

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

Events

edit

Elementary probability

edit

Meaning of probability

edit

Calculating with probabilities

edit

Independence

edit

(Related topics: measure theory)

Measure-theoretic probability

edit

Independence

edit

Conditional probability

edit

Discrete and continuous random variables

edit

Expectation

edit

Independence

edit

Some common distributions

edit

Some other distributions

edit

Functions of random variables

edit

Generating functions

edit

(Related topics: integral transforms)

Common generating functions

edit

Applications

edit

Convergence of random variables

edit

(Related topics: convergence)

Modes of convergence

edit

Applications

edit

Markov processes

edit

Stochastic differential equations

edit

See also

edit