Solution
= Solution
For rate $\lambda>0$,
$$
M_X(t)=\int_0^\infty\lambda e^{-(\lambda-t)x}dx
=\boxed{\frac\lambda{\lambda-t}},\qquad t<\lambda.
$$
This function is finite near zero, so its third derivative there equals the third moment. Therefore
$$
\boxed{\mathbb E(X^3)=M_X^{(3)}(0)=\frac6{\lambda^3}.}
$$