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Given there are two classes A and B and the prior probability of belonging to $ A = Na/N $ and $B = Nb/N $, I want to show that the linear discriminant analysis rule classifies an observation x to class B if:

$ x^TΣ(μ_{B} −μ_{A})> \frac{1}2μ^T_{B}Σ^{-1}μ_{B}−\frac{1}2μ^T_{A}Σμ_{A}+log(N_{A}/N) −log(N_{B}/N) $

I'm very new to this platform so I am unsure about how to code my math into this post! What I've done is attached my written attempt in a photo.

Is my line of thinking correct?

Any help at all would be greatly appreciated. Thank you!

enter image description here

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Yes, your reasoning is correct.

By the way, you can just use the same Latex syntax to write your math as you've done with the classification rule.

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