Solution
= Solution
Take $Y=X_1+X_2$. <Independence> factors the <expectation>:
$$
\boxed{\mathbb E(e^{tY})=\mathbb E(e^{tX_1})\mathbb E(e^{tX_2})=M_1(t)M_2(t).}
$$
= Solution
Take $Y=X_1+X_2$. <Independence> factors the <expectation>:
$$
\boxed{\mathbb E(e^{tY})=\mathbb E(e^{tX_1})\mathbb E(e^{tX_2})=M_1(t)M_2(t).}
$$