Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample co
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- enIn probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample co
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- enIn probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and the area under the entire curve is equal to 1. The terms "probability distribution function" and "probability function" have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, "probability distribution function" may be used when the probability distribution is defined as a function over general sets of values or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also used for the probability mass function, leading to further confusion. In general though, the PMF is used in the context of discrete random variables (random variables that take values on a countable set), while the PDF is used in the context of continuous random variables.
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- enProbability density function
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- Absolute continuity
- Almost everywhere
- Atomic orbital
- Bijective
- Borel set
- Cantor distribution
- Category:Equations of physics
- Category:Functions related to probability distributions
- Cauchy distribution
- Continuous or discrete variable
- Continuous probability distribution
- Continuous random variable
- Conversion of units
- Convolution
- Counting measure
- Cumulative distribution function
- Density estimation
- Derivative
- Differentiable function
- Dirac delta
- Dirac delta function
- Discrete random variable
- Distribution (mathematics)
- Expected value
- File:Boxplot vs PDF.svg
- File:Visualisation mode median mean.svg
- Function (mathematics)
- Generalized function
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- List of probability distributions
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- Probability theory
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- Standard normal distribution
- Statistical independence
- Statistical physics
- Univariate distribution
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- 4139581-5
- Função densidade
- Funció de densitat de probabilitat
- Función de densidad de probabilidad
- Función de densidade
- Función de densidá de probabilidá
- Fungsi dénsitas probabilitas
- Fungsi kepekatan probabilitas
- Fungsi ketumpatan kebarangkalian
- Funkcija gustine verovatnoće
- Funkcja gęstości prawdopodobieństwa
- Funzione di densità di probabilità
- Gostota verjetnosti
- Hàm mật độ xác suất
- Hustota pravděpodobnosti
- Kansdichtheid
- m.0bxcz
- Olasılık yoğunluk fonksiyonu
- Probabilitatearen dentsitate-funtzio
- Probability density function
- Probability density function
- Probablodensa funkcio
- Q207522
- Raspodjela vjerojatnosti
- Sandsynlighedstæthedsfunktion
- Sannsynstettleiksfunksjon
- Sűrűségfüggvény
- Täthetsfunktion
- Tetthetsfunksjon
- Þéttifall
- Tihedusfunktsioon
- Tiheysfunktio
- Variable aléatoire à densité
- Wahrscheinlichkeitsdichtefunktion
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- Συνάρτηση πυκνότητας πιθανότητας
- Густина ймовірності
- Плотность вероятности
- Плътност на вероятността
- Пулаяслăх йăвăлăхĕ
- Հավանականության խտություն
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- تابع چگالی احتمال
- دالة الكثافة الاحتمالية
- ალბათური განაწილების სიმკვრივე
- 機率密度函數
- 確率密度関数
- 확률 밀도 함수
- SeeAlso
- List of convolutions of probability distributions
- Product distribution
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- Category:Equations of physics
- Category:Functions related to probability distributions
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