Probability theory

Probability theory is the mathematical study of probability.

Related Topics:
Mathematical - Probability

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Mathematicians think of probabilities as numbers in the interval from 0 to 1 assigned to "events" whose occurrence or failure to occur is random. Probabilities P(E) are assigned to events E according to the probability axioms.

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The probability that an event E occurs given the known occurrence of an event F is the conditional probability of E given F; its numerical value is P(E cap F)/P(F) (as long as P(F) is nonzero). If the conditional probability of E given F is the same as the ("unconditional") probability of E, then E and F are said to be independent events. That this relation between E and F is symmetric may be seen more readily by realizing that it is the same as saying

Related Topics:
Conditional probability - Independent

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P(E cap F) = P(E)P(F).

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Two crucial concepts in the theory of probability are those of a random variable and of the probability distribution of a random variable; see those articles for more information.

Related Topics:
Random variable - Probability distribution

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