Consider $X$ to be a continuous random variable with distribution function $$F(x)=Pr[X\leq x]$$ Write down the distribution followed by random variable F(X).
My approach
$$Pr[F(X)\leq x]= Pr[X\leq F^{-1}(x)]=F(F^{-1}(x))=x$$ The answer given is uniform distribution on [0,1]. Can somebody explain where did i go wrong?