I believe your real issue is with computing variance.
I have actually given you the base formula to make you understand how this works. I will try again.
I have told you: Var(aX + bY) = a^2 Var(X) + b^2 Var(Y) + 2ab Cov(X, Y)
For 6.30: try plugging in a = 2 and b = -1 and use the fact that X & Y are independent. You will get variance as 5.
For exam type question, do this:
1. Set W = X1+X2+X3+X4. Compute Var(W) applying the above rule repeatedly.
2. Set V = Y1+Y2+Y3. Compute Var(V) applying the above rule repeatedly.
3. Now you will have linear combination of V and W as (V - W) with a = 1 and b = -1. Compute Var(V - W)
(Note all r.v. involved are independent of each other)
You will get variance of 31,000 in the end.
As you can see that the base principle works for every case.
So, I would again recommend that you do what I suggested earlier. I have a feeling you need to get the basics understood first and then you can try the sums.
Last edited: Mar 22, 2014