Consider two classes ${}_1$ and ${}_2$ with a priori probabilities $P({}_1)$ and $P({}_2).{}_1$ and ${}_2$

follow Gaussian distributions, that is$,p(x|{}_1)=N({}_1,{}_1)$ and $p(x|{}_2)=N({}_2,{}_2).$

Using Fisher's criterion ${?}^{FDR(w)}=\frac{w^T{S}_{b}w}{w^T{S}_{w}w}$ as given in the textbook, derive linear

discriminant analysis using ${}_1$ and ${}_2.$

Show under which condition the above linear discriminant is equivalent to $a$

Bayesian classifier.