I'm practicing for an exam and a mock question has me completely stumped. If someone could show me the steps I would be very grateful!
There are two random variables, $A$ and $B$. $Var(A) = 9$, and $Var(B) = 4$, and $Cov(A, B) = 2$.
a) What is $Var(2A - 3B + 10)$?
b) $U = A + B$, and $V = A + aB$, where $a$ is decided so $Cov(U, V) = 0$. What are the possible values of $a$?
c) $A$ and $B$ are simultaneously distributed with the Normal distribution, where $U$ and $V$ are the same as in the previous problem. What is $Cov(e^{sU}, e^{rV})$?