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08_ppt - Outline STAT 1302 Probability and Statistics II...

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Outline STAT 1302 Probability and Statistics II Example Class 8 Department of Statistics and Actuarial Science, University of Hong Kong [email protected] April 2008 Example Class 8, STAT 1302, By Catherine () Solution April 2008 1 / 14
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Outline Outline 1 Review 2 Question 1 3 Question 2 4 Question 3 Example Class 8, STAT 1302, By Catherine () Solution April 2008 2 / 14
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Review Question 1 Question 2 Question 3 Review 1 Likelihood ratio test (LR); Example Class 8, STAT 1302, By Catherine () Solution April 2008 3 / 14
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Review Question 1 Question 2 Question 3 Review 1 Likelihood ratio test (LR); 2 Uniformly most powerful (UMP) test; Example Class 8, STAT 1302, By Catherine () Solution April 2008 3 / 14
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Review Question 1 Question 2 Question 3 Review 1 Likelihood ratio test (LR); 2 Uniformly most powerful (UMP) test; 3 Generalized likelihood ratio (GLR) test; Example Class 8, STAT 1302, By Catherine () Solution April 2008 3 / 14
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Review Question 1 Question 2 Question 3 Review 1 Likelihood ratio test (LR); 2 Uniformly most powerful (UMP) test; 3 Generalized likelihood ratio (GLR) test; 4 Pearson Chi-Squared test. Example Class 8, STAT 1302, By Catherine () Solution April 2008 3 / 14
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Review Question 1 Question 2 Question 3 Question 1 (a) Denote θ 2 Θ 1 and θ 1 Θ 0 . Example Class 8, STAT 1302, By Catherine () Solution April 2008 4 / 14
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Review Question 1 Question 2 Question 3 Question 1 (a) Denote θ 2 Θ 1 and θ 1 Θ 0 . p ( x , θ 2 ) / p ( x , θ 1 ) = (Γ( θ 2 ) / Γ( θ 1 )) - n ( n Q i = 1 x i ) θ 2 - θ 1 Example Class 8, STAT 1302, By Catherine () Solution April 2008 4 / 14
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Review Question 1 Question 2 Question 3 Question 1 (a) Denote θ 2 Θ 1 and θ 1 Θ 0 . p ( x , θ 2 ) / p ( x , θ 1 ) = (Γ( θ 2 ) / Γ( θ 1 )) - n ( n Q i = 1 x i ) θ 2 - θ 1 θ 2 < θ 0 θ 1 , - ( θ 2 - θ 1 ) > 0.
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