If X and Y are exponentially distributed with the same parameter and they are also independent:

To compute the density function of :

Case 1) Z = X-Y with the constraint that X is strictly higher than Y, (X>Y)

Case 2) Z = X+Y without any constraint

If I want to do it by computing the cdf first:

Can someone explain which should be the limits in the following integral in both cases:

$\displaystyle

$$\displaystyle F_Z(z) = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty}f_X(x)f_Y(y) dx dy

$

Thanks in advance!