The pdf of an Exp(λ) random variable is given by f(x) = λe^{-λx} for x ≥ 0. So, for X and Y, we have:
f_X(x) = 2e^{-2x} \text{ for } x \ge 0
f_Y(y) = 2e^{-2y} \text{ for } y \ge 0
Now, we find the joint pdf f_{X,Y}(x,y):
f_{X,Y}(x,y) = f_X(x)f_Y(y) =
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