Problem%20Set%2003_2010_2011[1]

Problem%20Set%2003_2010_2011[1] - Middle East Technical...

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Middle East Technical University 2010-2011 Fall Department of Economics ECON 206 Instructor: Ozan ERUYGUR Research Assistant: Pelin AKÇAGÜN PROBLEM SET 03 CENTRAL LIMIT THEOREM PROBLEM 1 Let denote the sample variance for a random sample of ten ln(LC50) values for copper, and let denote the sample variance for a random sample of eight ln(LC50) values for lead, both samples using the same species of fish. The population variance for measurements on copper is assumed to be twice the corresponding population variance for measurements on lead. Assume to be independent of . 2 1 S 2 2 S 2 1 S 2 2 S a) Find a number b such that 2 1 2 2 .95 S Pb S ⎛⎞ ≤= ⎜⎟ ⎝⎠ b) Find a number a such that 2 1 2 2 .95 S Pa S [ Hint : Notice that () ( ) 12 21 // PU U k k 1 / ]. c) If a and b are as in the previous parts, find 2 1 2 2 S b S . PROBLEM 2 Let be a random sample of size 5 from a normal population with mean 0 and variance 1, and let , 5 , ..., YY Y 5 1 1/5 i i Y = = Y . Let be another independent observation from the same population. Let 6 Y Y 5 2 1 1 i W = = , and let ( ) 2 5 1 i i UY Y = =− . What is the distribution of U 22 6 25 / + ? Why?
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This note was uploaded on 03/22/2012 for the course ECON 106 taught by Professor Kücüksenel during the Spring '12 term at Middle East Technical University.

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Problem%20Set%2003_2010_2011[1] - Middle East Technical...

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