# Probability Theory

Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central 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. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.

As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.

### Other articles related to "probability theory":

Probability Theory - Central Limit Theorem
... The theorem states that the average of many independent and identically distributed random variables with finite variance tends towards a normal distribution irrespective of the distribution followed by the original random variables ... Formally, let be independent random variables with mean and variance Then the sequence of random variables converges in distribution to a standard normal random variable ...

### Famous quotes containing the words theory and/or probability:

[Anarchism] is the philosophy of the sovereignty of the individual. It is the theory of social harmony. It is the great, surging, living truth that is reconstructing the world, and that will usher in the Dawn.
Emma Goldman (1869–1940)

Liberty is a blessing so inestimable, that, wherever there appears any probability of recovering it, a nation may willingly run many hazards, and ought not even to repine at the greatest effusion of blood or dissipation of treasure.
David Hume (1711–1776)