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Unformatted text preview: Probability distribution From Wikipedia, the free encyclopedia Jump to: navigation , search This article is about probability distribution. For generalized functions in mathematical analysis, see Distribution (mathematics) . For other uses, see Distribution (disambiguation) . This article includes a list of references , related reading or external links , but its sources remain unclear because it lacks inline citations . Please improve this article by introducing more precise citations. (July 2011) This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (July 2011) In probability theory , a probability mass , probability density , or probability distribution is a function that describes the probability of a random variable taking certain values. For a more precise definition one needs to distinguish between discrete and continuous random variables. In the discrete case, one can easily assign a probability to each possible value: when throwing a die , each of the six values 1 to 6 has the probability 1/6. In contrast, when a random variable takes values from a continuum, probabilities are nonzero only if they refer to finite intervals: in quality control one might demand that the probability of a "500 g" package containing between 500 g and 510 g should be no less than 98%. Discrete probability distribution for the sum of two dice . Normal distribution , also called Gaussian or "bell curve", the most important continuous random distribution. If total order is defined for the random variable, the cumulative distribution function gives the probability that the random variable is not larger than a given value; it is the integral of the non cumulative distribution. Contents 1 Termin ology 1 . 1 B a s i c t e r m s 2 Discrete probabil ity distribut ion 2 . 1 C u m u l a t i v e d e n s i t y 2 . 2 D e [ edit ] Terminology As probability theory is used in quite diverse applications, terminology is not uniform and sometimes confusing. The following terms are used for noncumulative probability distribution functions: Probability mass , Probability mass function , p.m.f. : for discrete random variables. Categorical distribution : for discrete random variables with a finite set of values. Probability density , Probability density function , p.d.f : Most often reserved for continuous random variables. The following terms are somewhat ambiguous as they can refer to noncumulative or cumulative distributions, depending on authors' preferences: Probability distribution function : Continuous or discrete, noncumulative or cumulative....
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This note was uploaded on 02/23/2012 for the course STAT 598 taught by Professor Staff during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Staff
 Probability

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