Originally Posted by

**sfspitfire23** Hey guys-been struggling with this question the whole day-

Weekly downtime X (in hrs) for a certain industrial machine has approximately a gamma dist. with alpha=3.5 and beta=1.5. Loss L (in dollars) as a result of this downtime is given by $\displaystyle L=30X+2x^2$.

What is the expected value and variance of L?

So, I first set out to find an equation for $\displaystyle E(X^k)$ and I ended up with $\displaystyle \frac{\beta^k \Gamma(\alpha+k)}{\Gamma(\alpha)}$ and I am unsure how to proceed from here. Also, is my derivation correct?