Processing math: 100%

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pk(x)=πk12πσkexp(12σ2k(xμk)2)πl12πσlexp(12σ2l(xμl)2)log(pk(x))=log(πk)+log(12πσk)+12σ2k(xμk)2log(πl12πσlexp(12σ2l(xμl)2))log(pk(x))log(πl12πσlexp(12σ2l(xμl)2))=log(πk)+log(12πσk)+12σ2k(xμk)2δ(x)=log(πk)+log(12πσk)+12σ2k(xμk)2

As you can see, δ(x) is a quadratic function of x.