Chi-squared distribution

Definition:

• The chi-squared distribution often arises in practice as the distribution of the error involved in attempting to hit a target in n-dimensional space when each coordinate error is normally distributed.
• If $Z_1,Z_2,...,Z_n$ are independent standard normal random variables, then $Y=\sum _{i=1}^n{Z}_i^2$ is said to have the chi-squared distribution with $n$ degrees of freedom.