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September 5th, 2016, 10:32 AM   #1
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Neyman-Pearson criterion for two univariate normal distributions

Hi,,

I need help in solving this problem.Kindly provide me a way or procedure on how to solve it.No solution reqd

Consider the Neyman-Pearson criterion for two univariate normal distributions:
p(xj!i)  N(i; 2
i ) and P(!i) = 1=2 for i = 1; 2. Assume a zero-one error loss, and for convenience let 2 > 1.
(a) Suppose the maximum acceptable error rate for classifying a pattern that is actually in !1 as if it were in !2 is
E1. Determine the single-point decision boundary in terms of the variables given.
(b) For this boundary, what is the error rate for classifying !2 as !1?
(c) What is the overall error rate under zero-one loss?
(d) Apply your results to the specic case p(xj!1)  N(􀀀1; 1) and p(xj!2)  N(1; 1) and E1 = 0:05.
(e) Compare your result to the Bayes error rate (i.e., without the Neyman-Pearson conditions).

Kindly provide me a way or procedure on how to solve it.No solution reqd
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