using gamma random variable, how do you find the variance of L= 30Y + 2Y^2 given that alpha = 3 and beta = 2?
may i know what is the formula for V(Y^2) and how do i work out the formula in terms of alpha and beta?
Use $\displaystyle V(L)=E(L^2)-(E(L))^2$
$\displaystyle E(L^2)=E((30Y+2Y^2)^2)=900E(Y^2)+120E(Y^3)+4E(Y^4)$
Likewise, find $\displaystyle E(L)$
Use the MGF to obtain the moments of your gamma distribution.
If you haven't learned that yet, you coudluse wikipedia,
or use a thread here that found the k{th} moment for the gamma.