Consider the Neyman-Pearson criterion for two univariate normal distributions: p(x∣ω
i
​
)∼N(μ
i
​
,σ
i
2
​
) and P(ω
i
​
)=1/2 for i=1,2. Assume a zero-one error loss, and for convenience let μ
2
​
>μ
1
​
. (a) Suppose the maximum acceptable error rate for classifying a pattern that is actually in ω
1
​
as if it were in ω
2
​
is E
1
​
. Determine the single-point decision boundary in terms of the variables given.