If $\operatorname{Cov}(X_i,X_j) = ij$, find $\operatorname{Var}(X_1 + 2X_2 + 3X_3)$.
My attempt:
In general, $\operatorname{Var}(\sum_i X_i) = \sum_i\operatorname{Var}\left(A_i\right) + 2\sum_{i>j}\operatorname{Cov}\left(A_i,A_j\right)$
And $\operatorname{Var}(cX) = c^2\operatorname{Var}(X)$, also $\operatorname{Cov}(cX,Y) = c \operatorname{Cov}(X,Y)$
So $~\lower{6.25ex}{\begin{align}\operatorname{Var}(X_1 + 2X_2 + 3X_3) &= {\operatorname{Var}(X_1) + 2^2\operatorname{Var}(X_2) + 3^2\operatorname{Var}(X_3)\\ + 2{\times}2\operatorname{Cov}(X_1,X_2) + 3{\times}2\operatorname{Cov}(X_1,X_3) \\+ 2{\times}3{\times}2\operatorname{Cov}(X_2,X_3) }\\&= 1 + 16 + 81 + 8 + 18 + 72 \\&= 196\end{align}}$
I'm not sure if I'm correct though.