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100BHW4

# 100BHW4 - which leads to the maximum likelihood estimate...

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STAT 100B HWIV Problem 1. For two random variables X and Y , prove that corr ( X, Y ) 2 1. Problem 2. Let X 1 , ..., X n Exp( λ true ) independently, prove that among all the estimating equations of the form E λ ( h ( X )) = n i =1 h ( X i ) /n , the asymptotically most accurate estimate is given by the function h ( x ) =
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Unformatted text preview: , which leads to the maximum likelihood estimate. Problem 3. Prove that the likelihood ratio test is the most powerful test, that is, among all the tests with the same type I error, the likelihood ratio test has the smallest type II error....
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