Gamma Distribution

With shape $k>0$ and scale $\theta >0$:

$$f(x)=\frac{x^{k-1}{e}^{-x/\theta }}{\Gamma (k){\theta }^k},x>0$$

Expected Value

$$\mathbb{E}[X]=k\theta$$

Variance

$$\mathrm{Var}(X)=k{\theta }^2$$