# How to do this transformation $Y= g(x) \sim \mathcal U(0,2)$?

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 $Y\sim \mathcal U(0,2)$.

## 1 Answer

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.

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