Here's a fun fact Oded Schramm just told me: If X, Y, Z are independent and uniform on [0,1], then so is (XY)^Z. And here's a fun fact related to Archimedes' insight about the sphere and the cylinder: If X, Y, Z are independent Gaussians of mean 0 and variance 1, X/(X^2+Y^2+Z^2) is uniform on [0,1]. Since I'm teaching a course on simulation of stochastic processes this coming semester, these could serve as good homework problems of the "do a simulation, make a conjecture, try to prove it" variety. But I'd like a third homework problem where some simple combination of random variables LOOKS like it's uniform but ISN'T, so the students don't come away with the impression that "if it's roughly flat, it must be uniform". So: Does anyone know of a probability distribution that's close to uniform (or close to Gaussian, or something like that), but isn't? Jim Propp