Originally Posted by

**Robb** Hi all,

The length of time $\displaystyle Y $necessary to complete a key operation in the construction of houses has an exponential distribution with mean 10 hours. The formula $\displaystyle C=100+40Y+3Y^2$ relates the cost $\displaystyle C $of completeting this operation to the square of the time to completion. Find the mean and variance of $\displaystyle C$

So mean of C;

$\displaystyle E(C)=E(100+40Y+3Y^2)=100+40\cdot E(Y)+3\cdot [E(Y)]^2=100+40\cdot 10+3\cdot 100=800$

Just not sure I have calculated variance correctly;$\displaystyle E(C^2)=E[(100+40Y+3Y^2)^2]=$$\displaystyle E(100^2+1600Y^2+9Y^4+8000Y+600Y^2+240Y^3)=640000$

So $\displaystyle var(C)=640000-800^2=0$