Chi-Square Distribution

With $\nu >0$ degrees of freedom:

$$f(x)=\frac{1}{2^{\nu /2}\Gamma (\nu /2)}{x}^{\nu /2-1}{e}^{-x/2},x>0$$

Expected Value

$$\mathbb{E}[X]=\nu$$

Variance

$$\mathrm{Var}(X)=2\nu$$