[lisper]

This article takes a very long time to make an elementary point: if x is a uniformly distributed random variable, f(x) is not a uniformly distributed random variable if f is non-linear.

[doesnotexist]

Which is visualized nicely in these 20 second videos.

Non-linear transform of a random variable:

https://www.youtube.com/watch?v=hQjk4ClpuUk

Linear transform of a random variable:

https://www.youtube.com/watch?v=cKo6-DnIxCg