# Thread: Distribution of continuous random variable

1. ## 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!

2. ## Re: Distribution of continuous random variable

The most usual method for this question is to check the CDF of the resulting random variable against the CDF of ,
i.e. by considering

Playing around the inequality and the property of CDF shall give you the desired result.

Considering the derivative of CDF, i.e. the pdf will not be as trivial as that.

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