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If $X$ is a continuous random variable with probability density function $f_X(x)=2(1-x)$ for $0 < x < 1$, find the transformation $Y=g(X)$ such that the random variable $Y\sim \mathcal U(0,2)$.

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You could use the Probability Integral Transform to get the standard uniform distribution and then scale it accordingly. There might be other ways but I believe this is the fastest. Try it and let us know if you come across any problems.

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  • $\begingroup$ Exactly the approach I'd recommend. +1 $\endgroup$ – StatsStudent Jan 22 '16 at 22:30

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