Consider a circle of radius R, and

Consider a circle of radius R, and suppose that a point within the circle is randomly
chosen in such a manner that all regions within the circle of equal area are equally
likely to contain the point. (In other words, the point is uniformly distributed within
the circle.) If we let the center of the circle denote the origin and define X and Y to be
the coordinates of the point chosen (Figure 6.1), then, since (X, Y) is equally likely
to be near each point in the circle, it follows that the joint density function of X and
Y is given by