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If treating several random variables <math>X,Y,\ldots</math> etc. the corresponding letters are used as subscripts while, if treating only one, the subscript is usually omitted. It is conventional to use a capital <math>F</math> for a cumulative distribution function, in contrast to the lowercase <math>f</math> used for [[probability density function]]s and [[probability mass function]]s. This applies when discussing general distributions: some specific distributions have their own conventional notation, for example the [[normal distribution]].
The probability density function of a continuous random variable can be determined from the cumulative distribution function by differentiating<ref>{{Cite booktitle=Applied Statistics and Probability for Engineerslast1=Montgomeryfirst1=Douglas C.last2=Rungerfirst2=George C.publisher=John Wiley & Sons, Inc.year=2003isbn=0471204544page=104url=http://www.um.edu.ar/math/montgomery.pdf}}</ref> using the [[Fundamental Theorem of Calculus]]; i.e. given <math>F(x)</math>,
as long as the derivative exists.
▲: <math>f(x) = {dF(x) \over dx},</math> as long as the derivative exists.
The CDF of a [[continuous random variable]] <math>X</math> can be expressed as the integral of its probability density function <math>f_X</math> as follows:<ref name="KunIlPark" />{{rpp. 86}}

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