Suppose two classes of observations have means μ → 0 , μ → 1 {\displaystyle {\vec {\mu }}_{0},{\vec {\mu }}_{1}} and covariances Σ 0 , Σ 1 {\displaystyle \Sigma _{0},\Sigma _{1}} . Then the linear combination of features w → ⋅ x → {\displaystyle {\vec {w}}\cdot {\vec {x}}} will have means w → ⋅ μ → i {\displaystyle {\vec {w}}\cdot {\vec {\mu }}_{i}} and variances w → T Σ i w → {\displaystyle {\vec {w}}^{T}\Sigma _{i}{\vec {w}}} for i = 0 , 1 {\displaystyle i=0,1} . Fisher defined the separation between these two distributions to be the ratio of the variance between the classes to the variance within the classes: