Please, would you help?

(Optional) For two-group Bayes classification rule, express the population-level TPM using prior probabilities p, and p2, densities of the two populations fi (x) and f2(x), and the decision rules R, and R, derived in class. Assuming equal prior probability and equal misclassification cost, prove that with such choices of R, and Ro, for two normal distributions Np(uj, E) and No(#2. E). TPM = 4( 2 where ? = (1, -#2)'E-(#1 - #2), and $(.) is the CDF of standard normal random variables. (Hint: Consider the distribution of discriminant function.)