Suppose $X$ is a continuous random variable with a cumulative distributive function of $F(x)$. Let $Y$ be a variable such that $Y$ can be represented in terms of $X$, i.e $Y=F(X)$. Show that the probability density function of $Y$ represents a uniform distribution.
To begin I've tried to $G(y)$ be the CDF and $g(y)$ to be the PDF.
$\therefore G(y)=P(Y≤y)$
$=P(F(X)≤y)$
I can't progress from here (if this is even the right direction), any help would be greatly appreciated.
