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#[[pseudorandom number generator|Generate a random number]] <math>u</math> from the standard uniform distribution in the interval <math>[0,1]</math>, e.g. from <math>U \sim \mathrm{Unif}[0,1].</math>
#Find the [[cumulative distribution function#Inverse_distribution_function_(quantile_function)|generalized inverse]] of the desired CDF, i.e. <math>F_X^{-1}(u)</math>.
# Compute <math>X'(u)=F_X^{-1}(u)</math>. The computed random variable <math>X'(U)</math> has distribution <math>F_X</math> and thereby the same law as
Expressed differently, given a cumulative distribution function <math>F_X</math> and a uniform variable <math>U\in[0,1]</math>, the random variable <math>X = F_X^{-1}(U)</math> has the distribution <math>F_X</math>.<ref>{{cite book | last1 = McNeil | first1 = Alexander J. | last2 = Frey | first2 = Rüdiger | last3 = Embrechts | first3 = Paul | title = Quantitative risk management | date=2005 | series=Princeton Series in Finance | publisher=Princeton University Press, Princeton, NJ | page=186 | isbn=0-691-12255-5}}</ref>
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