# Math Help - Uniform distribution on a disk

1. ## Uniform distribution on a disk

Hey, I have a question:

This problem states that X and Y are uniformly distributed on the unit disk. It goes on to ask me questions like what is the joint density of the RVec X,Y, which is $\mathbf{1}_D\cdot \frac{1}{\pi}$... but then it asks questions specific to the individual variables.

For example, I am asked what $\mathbf{E}X$ is. Now, X is obviously not uniformly distributed; neither is y (if we take X,Y to be the x and y coordinates respectively).

Then if R is the distance from the point to the centre, find $\mathbf{E}R$ and Var(R).

Any tips/hints? I'm stuck on this one.

$x=r \cos \theta$
$y=r \sin \theta$