# Covariance of two products

#### tlitterio

##### New Member
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