Cumulative Distribution Functions

[genji]

Hi there,

I'm currently trying to review some concepts before a final. I have a sample question which is currently confusing me, and would appreciate some help.
The question goes:

Let X be a random variable with density fX and CDF FX, and let F^-1X be inverse function of FX.

Show that for the uniform distribution U over [0, 1], the distribution of the random variable F^-1X(U) is the same as that of X. Note that F^-1X is the inverse function of FX applied to U.

 

[Romsek]

Can you write down the CDF of the uniform[0,1] distribution?

 

[genji]

It should be P(U <= x) = x, if I remember correctly

 

[Romsek]

It should be P(U <= x) = x, if I remember correctly

and what is [MATH]f^{-1}(x)[/MATH] ?