Cov and Var need help!

[munnaal]

Hi guys!
I am taking intro to SEM class. I need help regarding the Cov and Var matrix which I try hard to understand through this class.

X, Y, Z, and W are random variables with the same variance of 1.5 then Covariances: Cov(X,Y) = .5; Cov(Z,W) = .6 = Cov(X,W), Cov(Y,Z) = .3. Then I have to find the following
cov(s) and var(s)
1) Var(X+2Y),
2) Var(3Z+4W),
3) Cov(2X+3Z, 5Y+3W)
4) Cov(3Y+2W, 5X+1.5Z)

Thank you in advance

 

[munnaal]

For the first question, is it correct?
Var(x+2y) = Var(x) + 4Var(y)+ 4Cov(x,y)
= 1.5+4(1.5)+4(0.5)
=9.5

 

[SliceandDice221]

You got #1 right so you probably won't need help with 2.

For #3 and #4, I recommend using the definition of covariance to see what is going on. Recall that if A and B are random variables,

Cov(A,B) = E(AB)-E(A)E(B)

You'll see that after some simplification, you will arrive at an answer in terms of the individual covariance terms. So, for #3 you should see that your answer takes the form:

10Cov(X,Y) + 6Cov(X,W) + 15Cov(Y,Z) + 9Cov(W,Z)