$f_Z(z) = \int_{-\infty}^{\infty} f_X(x) f_Y(z-x) dx$

$f_Z(z) = \int_{-\infty}^{\infty} f_X(x) f_Y(z+x) dx$

$f_Z(z) = f_X(z) + f_Y(z)$

$f_Z(z) = f_X(z) f_Y(z)$