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P(X / C1) = \frac{1}{\sqrt{2\pi}} \left(\exp{-\frac{x^{2}}{2}}\right) P(X ...

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$P(X / C1) = \frac{1}{\sqrt{2\pi}} \left(\exp{-\frac{x^{2}}{2}}\right)$ P(X / C1) = \frac{1}{\sqrt{2\pi}} \left(\exp{-\frac{x^{2}}{2}}\right)

$P(X / C2) = \frac{1}{\2/sqrt{2\pi}} \left(\exp{-\frac{x^{2}}{8}}\right)$ P(X / C2) = \frac{1}{\2/sqrt{2\pi}} \left(\exp{-\frac{x^{2}}{8}}\right)

Find the optimum decision rule in the sense of minimizing the total probability of error in terms of the likelihood ratio l(x).

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