“probability density function”的概念、定义、翻译、参考文献-科学参考

probability density function

Mathematics

For a continuous random variable X, a probability density function (or pdf) of X is the function f_X such that

$Pr (a \leq X \leq b) = \int_{a}^{b} f_{X} (x) d x .$

A probability density function is necessarily non-negative with integral 1. The Cantor distribution is an example of a continuous random variable which does not have a probability density function.

Suppose that, for the random variable X, a sample is taken and a corresponding histogram is drawn with class intervals of a certain width. Then, loosely speaking, as the number of observations increases and the width of the class intervals decreases, the histogram assumes more closely the shape of the graph of the probability density function.

Statistics

For a continuous random variable X the probability density function f is such that $probability density function$ for all x₁<x₂. Because, for a continuous random variable, P(X=x_j)=0 for any value x_j, either or both of the ‘<’ signs in the left-hand side can be replaced with ‘≤’. If the interval of possible values for X is (a, b), then $probability density function$ It is often convenient to regard the function f as being defined for all real values of x. This can be achieved by taking f(x)=0 for x outside the interval (a, b), so that $probability density function$ This property, and the property that f(x)≥0 for all x, are essential properties of a probability density function. It should be noted that, although f(x) is related to probability, f(x) can exceed 1.
The probability density function is often referred to simply as the probability density. It is related to the cumulative distribution function F by $probability density function$ The probability density function is not necessarily continuous. At a point of discontinuity the value assigned to f(x) is immaterial.

Geology and Earth Sciences

In statistics, the mathematical function which allocates probabilities of particular observations occurring. The probability density function may be used to construct a frequency distribution of certain events occurring either discretely, in the form of a histogram, or continuously.

单词	probability density function
释义	probability density function Mathematics For a continuous random variable X, a probability density function (or pdf) of X is the function f_X such that $Pr (a \leq X \leq b) = \int_{a}^{b} f_{X} (x) d x .$ A probability density function is necessarily non-negative with integral 1. The Cantor distribution is an example of a continuous random variable which does not have a probability density function. Suppose that, for the random variable X, a sample is taken and a corresponding histogram is drawn with class intervals of a certain width. Then, loosely speaking, as the number of observations increases and the width of the class intervals decreases, the histogram assumes more closely the shape of the graph of the probability density function. Statistics For a continuous random variable X the probability density function f is such that $probability density function$ for all x₁<x₂. Because, for a continuous random variable, P(X=x_j)=0 for any value x_j, either or both of the ‘<’ signs in the left-hand side can be replaced with ‘≤’. If the interval of possible values for X is (a, b), then $probability density function$ It is often convenient to regard the function f as being defined for all real values of x. This can be achieved by taking f(x)=0 for x outside the interval (a, b), so that $probability density function$ This property, and the property that f(x)≥0 for all x, are essential properties of a probability density function. It should be noted that, although f(x) is related to probability, f(x) can exceed 1. The probability density function is often referred to simply as the probability density. It is related to the cumulative distribution function F by $probability density function$ The probability density function is not necessarily continuous. At a point of discontinuity the value assigned to f(x) is immaterial. Geology and Earth Sciences In statistics, the mathematical function which allocates probabilities of particular observations occurring. The probability density function may be used to construct a frequency distribution of certain events occurring either discretely, in the form of a histogram, or continuously.
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