Suppose that $\displaystyle (X_i, Y_i), i = 1,...,n$ is a 2D sample, with each $\displaystyle (X_i, Y_i)$ assumed to be uniformly distributed in a circle centered at the origin of an unknown radius $\displaystyle r$.

How do I calculate the pdf of this?

I'm thinking $\displaystyle \frac{1}{\pi r^2}$ but I don't think this is correct.