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'''List of Probability Topics'''

Probability theory is a branch of mathematics concerned with analyzing random phenomena. The fundamental objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. This article aims to provide a comprehensive list of topics related to probability theory, each of which plays a crucial role in understanding the behavior of systems affected by randomness.

== Basic Concepts ==
* [[Probability Space]]: The mathematical construct that models a random experiment. It consists of a sample space, a set of events, and a probability measure.
* [[Random Variable]]: A variable whose possible values are numerical outcomes of a random phenomenon.
* [[Probability Distribution]]: Describes how probabilities are distributed over the values of the random variable.
* [[Expected Value]]: The weighted average of all possible values that a random variable can take on.
* [[Variance]] and [[Standard Deviation]]: Measures of how spread out the values of a random variable are.
* [[Law of Large Numbers]]: A theorem that describes the result of performing the same experiment a large number of times.
* [[Central Limit Theorem]]: States that, under certain conditions, the sum of a large number of random variables will be approximately normally distributed.

== Probability Distributions ==
* [[Binomial Distribution]]: The probability distribution of the number of successes in a sequence of independent experiments.
* [[Poisson Distribution]]: A discrete frequency distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.
* [[Normal Distribution]] (Gaussian distribution): A very common continuous probability distribution - symmetric and bell-shaped.
* [[Exponential Distribution]]: The probability distribution that describes the time between events in a Poisson point process.
* [[Gamma Distribution]]: A two-parameter family of continuous probability distributions.

== Stochastic Processes ==
* [[Markov Chains]]: Models of random processes that undergo transitions from one state to another on a state space.
* [[Brownian Motion]]: A continuous-time stochastic process used to model random movement.
* [[Poisson Process]]: A stochastic process that models a series of events occurring at random points in time.
* [[Random Walk]]: A mathematical formalization of a path that consists of a succession of random steps.

== Advanced Topics ==
* [[Bayesian Probability]]: Interpretation of probability where probability expresses a degree of belief in an event.
* [[Monte Carlo Methods]]: A broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.
* [[Stochastic Differential Equations]]: Differential equations in which one or more of the terms is a stochastic process.
* [[Queueing Theory]]: The mathematical study of waiting lines, or queues.

== Applications ==
Probability theory is applied in a wide variety of fields, including [[Statistics]], [[Finance]], [[Gambling]], [[Science]], [[Engineering]], and [[Information Technology]].

[[Category:Probability Theory]]
[[Category:Mathematics]]
[[Category:Statistical Theory]]

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