quiz3AS-M_f10 - Section M Quiz 3 Version A ECON 506,...

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Unformatted text preview: Section M Quiz 3 Version A ECON 506, Section M Solution NAME: ___Ali Toossi_________________ Quiz 3, Version A November 11 2010 NetID: ______________________________ Total points: 50 I. ( 10 points) Let < <- = elsewhere x x f , 1 1 , 5 . ) ( be the p.d.f. of the random variable X. Define the random variable Y by 2 X Y = . Use the method of distribution functions to find the p.d.f. of Y Solution: = < = - = = = - y 1 , 1 1 , 5 . , ) ( ) ( ) ( ) ( 2 y y dx y y X y P y X P y Y P y G y y < < = Elsewhere 0, 1 y , 2 1 ) ( y y g II. Let X and Y have the joint p.d.f. < < < = elsewhere y x y x f , 1 , 2 ) , ( (a) ( 8 points) Find the conditional p.d.f of X , given y Y = Solution: First we have to find the marginal p.d.f of Y 1 y , 2 2 ) ( < < = = y dx y f y Y 1 y y; x , 1 2 2 ) | ( | < < < < = = y y y x f Y X (b) ( 5 points) Find the conditional mean of X , given y Y = Solution: 1 y , 2 ) | (...
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quiz3AS-M_f10 - Section M Quiz 3 Version A ECON 506,...

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