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probability generating function

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  • Probability-generating function — In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are… …   Wikipedia

  • Probability density function — Boxplot and probability density function of a normal distribution N(0, σ2). In probability theory, a probability density function (pdf), or density of a continuous random variable is a function that describes the relative likelihood for this… …   Wikipedia

  • Generating function — This article is about generating functions in mathematics. For generating functions in classical mechanics, see Generating function (physics). For signalling molecule, see Epidermal growth factor. In mathematics, a generating function is a formal …   Wikipedia

  • Moment-generating function — In probability theory and statistics, the moment generating function of any random variable is an alternative definition of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with… …   Wikipedia

  • Factorial moment generating function — In probability theory and statistics, the factorial moment generating function of the probability distribution of a real valued random variable X is defined as:M X(t)=operatorname{E}igl [t^{X}igr] for all complex numbers t for which this… …   Wikipedia

  • Coupon collector's problem (generating function approach) — The coupon collector s problem can be solved in several different ways. The generating function approach is a combinatorial technique that allows to obtain precise results. We introduce the probability generating function (PGF) G(z) where… …   Wikipedia

  • Probability distribution — This article is about probability distribution. For generalized functions in mathematical analysis, see Distribution (mathematics). For other uses, see Distribution (disambiguation). In probability theory, a probability mass, probability density …   Wikipedia

  • Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …   Wikipedia

  • Cumulative distribution function — for the normal distributions in the image below …   Wikipedia

  • List of probability topics — This is a list of probability topics, by Wikipedia page. It overlaps with the (alphabetical) list of statistical topics. There are also the list of probabilists and list of statisticians.General aspects*Probability *Randomness, Pseudorandomness,… …   Wikipedia

  • Examples of generating functions — The following examples are in the spirit of George Pólya, who advocated learning mathematics by doing and re capitulating as many examples and proofs as possible. The purpose of this article is to present common tricks of the trade in context, so …   Wikipedia

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