Covariance of two products

#1
Covariance of two products

I am in a stats class and the professor has asked us to calculate the covariance and the standard deviation of the total revenue. I was given the below information:

X
Unit Price = $10
E[X] = 10,000
Var(X) = 1,000,000

Y
Unit Price = $5
E[Y] = 7,000
Var(Y) = 800,000

I have calculated
X
StDev(X) = 1,000
E[X-Revenue] = $100,000
Var(X-Rev) = 100,000,000
StDev(X-Rev) = $10,000

Y
StDev(Y) = 894
E[Y-Revenue] = $35,000
Var(Y-Rev) = 20,000,000
StDev(X-Rev) = $4,472

X,Y
Var(X+Y) = 120,000,000
StDev(X+Y) = $10,954
Corr(X,Y)= 0.70
E[H+M]= $135,000
Cov(X,Y) = 626,099
StDev(Cov(X,Y)) $791.26

Questions:
1. Is the Covariance correct? (I calculated it by multiplying .7*(Sqrt(1,000,000)*Sqrt(800,000)) is this correct)
2. What is the difference between Var(X+Y) and Cov(X,Y)?
3. If there was no correlation coefficient, would Var(X+Y) = Cov(X,Y)?
4. The $791.26 is just the square root of the Cov(X,Y), when I was doing this, I thought that might be the standard deviation of the total revenue, but in writing this, I think that might be incorrect. What does this number represent? DOes it mean anything?
5. Is the standard deviation of the total revenue the StDev(X+Y)?


Any help would be greatly appreciated!

Thanks!
Tony