The Value Of $\chi$ ² with V Degrees of Freedom Such That the Area

The value of $\chi$ ² with v degrees of freedom such that the area to its right under the chi-squared curve is equal to A is denoted by $\chi _ { A , v } ^ { 2 }$ , while $\chi _ { 1 - A , v } ^ { 2 }$
denotes the value such that the area to its left is A.