The problem is this:

I have been given a continuous random variable X with pdf=P, cdf=F and quantile function q.

I now consider the transformed random variable Y=F(X), and I have to show that Y is uniformly distributed on the interval [0,1].

My first thoughts was to use the formula for pdf of Y=t(X), that is

t(y)=p(t^-1(y))* d/dy t^-1(y)

which gives me

t(y)=p(q(y))*q´(y)

Is it correct to assume that I am trying to get this to equal 1? And how do I proceed from here?

Thank you!