Cumulative distribution function: Difference between revisions

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[[File:Normal Distribution CDF.svg|thumb|300px|Cumulative distribution function for the [[normal distribution]]]]
In [[probability theory]] and [[statistics]], the '''cumulative distribution function''' ('''CDF''') of a real-valued [[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 book|url=|title=Mathematics for Machine Learning|last=Deisenroth,Faisal,Ong|first=Marc Peter,A Aldo, Cheng Soon|publisher=Cambridge University Press|year=2019|isbn=9781108455145|location=|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.