Let A be the subset of the plane R2 defined as the intersection of the first quadrant and the annulus between the circles of radii 1 and 2 centered at the origin. In other words
A = {(x, y) | x ? 0, y ? 0, 1 ? x2 + y2 ? 4}.
Let (X, Y ) be a uniformly chosen point in the region A.
Find the marginal density (PDF) and the expected value of the first coordinate X.