100BHWF - H ? Find the decision rule that has the minimum...

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STAT 100B Final Homework Due Friday Problem 1: Suppose we want to test H 0 : X p 0 ( x ) versus H 1 : X p 1 ( x ). Suppose the prior probability Pr( H 1 ) = λ = 1 - Pr( H 0 ). (1) Calculate the posterior probability Pr( H 1 | X = x ). (2) Suppose the loss for type I error is l 1 and the loss for type II error is l 2 . If X = x , then what is the risk of accepting H 0 and what is the risk of rejecting
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Unformatted text preview: H ? Find the decision rule that has the minimum risk. Problem 2: Continue from Problem 1. Suppose p ( x ) is N ( , 2 ), and p 1 ( x ) is N ( 1 , 2 ). Prove that log(Pr( H 1 | X = x ) / Pr( H | X = x )) = + x for some and . 1...
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This note was uploaded on 01/27/2011 for the course STATS 100b taught by Professor Staff during the Fall '08 term at UCLA.

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