12.1 Notation

The notation for the chi-square distribution is:

${\chi }^2$ ~ ${\chi }_{\text{df}}^2$

where $\mathrm{df}=$ degrees of freedom depend on how chi-square is being used. (If you want to practice calculating chi-square probabilities then use $\mathrm{df}=n-1$ . The degrees of freedom for the three major uses are each calculated differently.)

For the ${\chi }^2$ distribution, the population mean is $\mu =\mathrm{df}$ and the population standard deviation is $\sigma =\sqrt{2\cdot \mathrm{df}}$ .

The random variable is shown as ${\chi }^2$ but may be any upper case letter.

The random variable for a chi-square distribution with $k$ degrees of freedom is the sum of $k$ independent, squared standard normal variables.

${\chi }^2=(Z_1{)}^2+(Z_2{)}^2+...+(Z_k{)}^2$