Let XXX have PDF f(x)=e−xf(x) = e^{-x}f(x)=e−x for x≥0x \ge 0x≥0. Find the MGF MX(t)M_X(t)MX(t).
(1−t)−1(1-t)^{-1}(1−t)−1
(1−t)(1-t)(1−t)
(1+t)−1(1+t)^{-1}(1+t)−1
(1−t)−2(1-t)^{-2}(1−t)−2