Inverse transform sampling: Difference between revisions

Revision as of 05:43, 17 January 2006

Revision as of 18:45, 20 January 2006

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:<math>= \Pr(\inf\;\{x \mid F(x)=U\} \leq x) \!</math> &nbsp;&nbsp; (by the definition of <math>F^{-1}</math>)

:<math>= \Pr(U \leq F(x)) \!</math> &nbsp;&nbsp; (applying ''F'', which is [[monotonic function|monotonic]], to both sides)

:<math>= F(x) \!</math> &nbsp;&nbsp; (because <math>\Pr(U \leq y) = y</math>, since ''U'' is uniform on the unit interval)

==References==