Chi-Squared Distribution Probabilities


degrees of freedom

$$\Large \nu$$
$$\chi_\nu^2$$
$$f(z) = \frac{1}{\Gamma \left( \frac{\nu}{2} \right) \ 2^{\frac{\nu}{2}}} \ z^{\frac{\nu}{2} - 1} \ \exp \left( -\frac{z}{2} \right)$$

Area


a

b


area

$$\int_a^b f(x) \ dx$$

0.05

Score from Tail Area


tail area

$$A$$

bound

$$x0 : \ \int_{x0}^\infty f(x) \ dx = A$$

0.05