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