My Math Forum Neyman-Pearson criterion for two univariate normal distributions

 September 5th, 2016, 10:32 AM #1 Newbie   Joined: Sep 2016 From: US Posts: 1 Thanks: 0 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 specic 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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