Thread: 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 ... but then it asks questions specific to the individual variables.

For example, I am asked what 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 and Var(R).

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

Thanks in advance!

Use Polar