Outline of probability

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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]

Probability theory[edit]

(Related topics: measure theory)

Measure-theoretic probability[edit]

Independence[edit]

Conditional probability[edit]

Random variables[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]

Stochastic processes[edit]

Some common stochastic processes[edit]

Markov processes[edit]

Stochastic differential equations[edit]

Time series[edit]

Martingales[edit]

See also[edit]