Chi-Squared Distribution

A probability distribution \(Chi^2(k)\) governing the sum of \(k\) squared independent standard normal random variables \(Z_i\), defined by
\[ X^2_k = \sum_{i=0}^{k-1} Z_i^2 \]
where \(\sum\) is the summation sign and each \(Z_i\) are independent standard normal random variables.