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Suppose that $X$ has a pdf $f(x)=2x$ on $[0,1]$ (and zero otherwise), and let $U$ be a uniform random variable on $[0,1]$. Find a function $g$ such that $g(U)$ and $X$ have the same distribution (behaviour).

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    http://math.stackexchange.com/questions/33922/what-exactly-is-the-probability-integral-transform2012-01-26

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