F Distribution

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The random variable defined by

$$F_{n,m}=\frac{{\chi }_n^2/n}{{\chi }_m^2/m}$$

is said to have an F-distribution with $n,m$ degrees of freedom.

• Parameters
  • $n,m\in \mathbb{N}$
• Mean
  • $m/(m-2)$
• Variance
  • $\frac{2m^2(m+n-2)}{n(m-2{)}^2(m-4)}$
• MGF
  • Undefined