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[[File:Normal Distribution CDF.svgthumb300pxCumulative distribution function for the [[normal distribution]]]]
In [[probability theory]] and [[statistics]], the '''cumulative distribution function''' ('''CDF''') of a realvalued [[random variable]] <math>X</math>, or just '''distribution function''' of <math>X</math>, evaluated at <math>x</math>, is the [[probability]] that <math>X</math> will take a value less than or equal to <math>x</math>.<ref>{{Cite bookurl=https://github.com/mmlbook/mmlbook.github.iotitle=Mathematics for Machine Learninglast=Deisenroth,Faisal,Ongfirst=Marc Peter,A Aldo, Cheng Soonpublisher=Cambridge University Pressyear=2019isbn=9781108455145location=pages=181}}</ref>
In the case of a scalar [[continuous distribution]], it gives the area under the [[probability density function]] from minus infinity to <math>x</math>. Cumulative distribution functions are also used to specify the distribution of [[multivariate random variable]]s.

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