Let \(X\) and \(Y\) be jointly absolutely continuous with density

\[ f_{XY}(x,\, y)=\frac{1}{\pi},\quad x^2+y^2\leq 1. \]

So \(X\) and \(Y\) jointly possess the uniform distribution on the unit disc.

1. The joint density is a surface in three-dimensional space. Sketch what the joint density looks like.
2. Compute the marginal densities of \(X\) and \(Y\).
3. Are \(X\) and \(Y\) independent?