F Distribution

Definition

• With $X,Y$ as Independent Random Variable
• With $X\sim {\mathcal{X}}_{(m)}^2$
• With $Y\sim {\mathcal{X}}_{(n)}^2$
• Then, $\frac{\frac{X}{m}}{\frac{Y}{n}}\sim F$ distribution with degrees of freedom $(m,n)$

Properties

• $W\sim F(m,n)⟹\frac{1}{W}\sim F(n,m)$