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distribution function

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable ${\\displaystyle X}$ , or just distribution function of ${\\displaystyle X}$ , evaluated at ${\\displaystyle x}$ , is the probability that ${\\displaystyle X}$ will take a value less than or equal to ${\\displaystyle x}$ .
Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) ${\\displaystyle F\\colon \\mathbb {R} \ ightarrow [0,1]}$ satisfying ${\\displaystyle \\lim _{x\ ightarrow -\\infty }F(x)=0}$ and ${\\displaystyle \\lim _{x\ ightarrow \\infty }F(x)=1}$ .
In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to ${\\displaystyle x}$ . Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Cumulative_distribution_function)

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