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3.2 Transformation of pdf's     continued...

Perhaps the most important transformation occurs when is the cumulative distribution function, or cdf:

In this case, we have , and one finds the important result that the pdf for the transformation is given by:

In other words, the cdf is always uniformly distributed on [0,1], independently of the pdf ! Any value for the cdf is equally likely on the interval [0,1]. As will be seen next, this result has important ramifications for sampling from an arbitrary pdf.