If we have that both $X_1$ and $X_2$ are gamma(r,$\lambda$) distributed where $\lambda$ is the rate so the density is $\Gamma(r)^{-1}\lambda^rx^{r-1}e^{-\lambda x}$. What is the distribution of $-(aX_1+bX_2)$, where both a and b are positive constants.
My thought was that $aX_1 \sim gamma(r,a\cdot\lambda)$ and $bX_2 \sim gamma(r,b\cdot\lambda)$ by using the "scaling-property" but then I get stock because, I dont know how the sum of them is distributed (with a minus sign).