Cumulative distribution function: Difference between revisions

The probability density function of a continuous random variable can be determined from the cumulative distribution function by differentiating.
 
[[Probability density function|Probability Density Function]] from the Cumulativecumulative Distributiondistribution Functionfunction<ref>{{Cite book|title=Applied Statistics and Probability for Engineers|last=|first=|publisher=|year=|isbn=1119456266|location=|pages=70}}</ref>
 
Given ''F''(''x''),
 
''f (x) ='' <math>{dF(x) \over dx}</math>, as long as the derivative exists.
 
''f (x) ='': <math>{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" />{{rp|p. 86}}