
Distribution of continuous random variable
Hi all, I have been struggling with this problem for quite a while now and I am getting nowhere
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!


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