Finding the Expected Value and Variance of Random Variables This is an introductory math finance course, and for some reason, my prof has decided to ask us this question. We haven't learnt this type of material yet, and our textbook is close to NO help. If anyone has a clue on how to solve this problem, PLEASE help me! :)
Assume $X_1$, $X_2$, $X_3$ are random variables with the following quantitative characteristics:
$E(X_1) = 2$, $E(X_2) = -1$, $E(X_3) = 4$; $Var(X_1) = 4$, $Var(X_2) = 6$, $Var(X_3) = 8$;
$COV(X_1,X_2) = 1$, $COV(X_1,X_3) = -1$, $COV(X_2,X_3) = 0$
Find $E(3X_1 + 4X_2 - 6X_3)$  and  $Var(3X_1 + 4X_2 - 6X_3)$.

Well, just to expand on mne__povezlo's answer, I guess a more complete (and useful, in your case) formula for variance would be:
$$\mathrm{Var}\left(\sum_{i=1}^{n}a_{i}X_{i}\right)=\sum^n_{i=1}a_{i}^2\mathrm{Var}X_{i}+2\underset{1\le{i}<j\le{n}}{\sum\sum}a_{i}a_{j}\mathrm{Cov}\left(X_i,X_{j}\right)$$
Now what's left is just to plug in your numbers into the formula.
