Consider a sphere of radius $R$ centered at the origin with points uniformly distributed on the surface. What is the marginal pdf of the x-coordinate of these points?
Apparently the answer is
$$ f_X(x) = \frac{1}{2R} $$
This is very unintuitive for me because I would think this $f_X$ would be dependent on $x$, and would be largest at $x = 0$ tapering off as x increases/decreases.