Moments

$\mathbb{E}[aX+b] = a\mathbb{E}[X] + b$

$\mathbb{V}[aX+b] = a^2 \mathbb{V}{X}$

$X \sim \gamma(\alpha, \theta)$, $\mathbb{E}[X^k] = {\Gamma(\alpha+k) \over \Gamma(\alpha)} \theta^k$

$\Gamma(\alpha+1) = \alpha \Gamma(\alpha)$, $\Gamma(1) = 1,~\Gamma({1 \over 2}) = \sqrt{\pi}$