I have a set of random variables $X_1$, $X_2$, $X_3$, ... $X_n$. They are continuous and $0 \leq X_i \leq 1$. And Let's assume they are i.i.d from the same distribution.
How do I evaluate the KL-divergence (or other distance metric defined over PDFs) between the distribution of these random variables to a uniform distribution? (if calculating the PDF of these random variables first is not an option).