Find the density function of X +Y , where X and Y have a joint density as given in Examp...

Find the density function of X +Y , where X and Y have a joint density as given in Example D in Section 3.3.

Reference

Consider the following joint density:

This joint density is plotted in Figure 3.7. To find the marginal densities, it is helpful to drawa picture showing where the density is nonzero to aid in determining the limits of integration (see Figure 3.8).

In some applications, it is useful to analyze distributions that are uniform over some region of space. For example, in the plane, the random point (X, Y ) is uniform over a region, R, if for any A ⊂ R,