I'm not sure about my solution for following question:
A shop is selling item $X_1$ on an average day 20 times for 2\$ with $\sigma_1=5$. Item $X_2$ is sold 40 times for 3\$ with $\sigma_2=10$. You have 100\ fixed costs. What can you say about the income? (sorry for the bad english)
I started with: (D=daily income)
D=20 \cdot X_1+40 \cdot X_2 - 100
E(D)=E(20 \cdot X_1+40 \cdot X_2 - 100)=E(20 \cdot X_1)+E(40 \cdot X_2)+E(-100)= 20 \cdot E(X_1)+40 \cdot E(X_2) - 100 = 20 \cdot 2 + 40 \cdot 3 - 100 = 60
60\ daily income seems logical.
$Var(D)=Var(20 \cdot X_1+40 \cdot X_2 - 100)=Var(20 \cdot X_1)+Var(40 \cdot X_2)+Var(-100)= 400 \cdot Var(X_1) + 1600 \cdot Var(X_2) = 400 \cdot 25 + 1600 \cdot 100 = 170.000$
That seems very unrealistic. Where is my mistake?
Thanks a lot in advance.