Chi-squared Distribution

Notation:

$X \sim \chi^{2}_{(k)}$

Probability Density Function:

$f(x)=\frac{1}{2^{k/2}\Gamma \left( \frac{k}{2} \right) } x^{k/2-1} e^{-x/2}$

where:

Mean:

$\mathrm{E}[X]=\mu=k$

Variance:

$\mathrm{Var}[X]=\sigma^2=2k$

References:

  1. Chi-squared Distribution - Wikipedia
  2. Chi-squared Distribution - Wolfram MathWorld