Solution
= Solution
{c}
Assume finite second moments and write $Z_i=X_i-\mathbb E X_i$. Expanding the square in the definition of <variance> gives
$$
\operatorname{Var}(X_1+X_2)=\mathbb E[(Z_1+Z_2)^2]
=\mathbb E Z_1^2+\mathbb E Z_2^2+2\mathbb E(Z_1Z_2).
$$
Recognizing the two <variances> and the <covariance>, we obtain
$$
\boxed{\operatorname{Var}(X_1+X_2)=\operatorname{Var}(X_1)+\operatorname{Var}(X_2)+2\operatorname{Cov}(X_1,X_2).}
$$