Unformatted text preview: student wants to design a new type of True of False question with a third response, the “I give up”
response. We will model this as a hypothesis testing problem, where the true answer is obscured by ”noise” in the
student’s head.
H0 : the “false” hypothesis, s = −1, P0 = 1/2
H1 : the “true” hypothesis, s = +1, P1 = 1/2 We observe y = s + v , where v ∼ N (0, 2) is the noise in the student’s head, modeled as a Gaussian RV. The
student can decide H0 , H1 or can “give up”. The costs of these are as follows:
• If the student chooses Hi but Hj is true then Cij = 1 if i = j and 0 otherwise.
• If the student decides to “give up” the cost incurred is 1/4.
Find the decision rule that the student should use to process his muddles thoughts (y ) in order to minimize his
expected cost, expressing this rule in the simplest form possible. 5 Boston University Department of Electrical and Computer Engineering 5. Given two random variables X SC505, STOCHASTICgenerally gives us information about the r...
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This note was uploaded on 01/08/2013 for the course ECE 531 taught by Professor Natasha during the Spring '10 term at Ill. Chicago.
 Spring '10
 Natasha

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