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quiz3AS-M1_f10

# quiz3AS-M1_f10 - Section M1 ECON 506 Section M1 Quiz 3...

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Section M1 Quiz 3 Version A ECON 506, Section M1 Solution NAME: ___Ali Toossi_________________ Quiz 3, Version A November 11 2010 NetID: ______________________________ Total points: 50 I. ( 10 points) Let 0 , 1 0 , ) ( 1 < < = - θ θ θ x x x f be the p.d.f. of the random variable X. Define the random variable Y by X Y ln 2 θ - = . Use the method of transformations to find the p.d.f. of Y Solution: θ θ θ 2 2 2 1 Y Y e dY dX e X - - - = = 0 , 2 1 2 1 ) ( 2 2 1 2 = = - - - - y e e e y g y Y Y θ θ θ θ θ II. Let X and Y have the joint p.d.f. 1 1 ; 1 1 |), | 1 ( 2 3 ) , ( 2 < < - < < - - = y x y x y x f (a) ( 8 points) Let A = {(x, y): 0<x<1, 0<y<x}. Find the ]. ) , [( A Y X P ε Solution: 40 9 10 4 2 3 ) 2 ( 2 3 2 2 3 ) 1 ( 2 3 ] ) , [( 1 0 5 4 1 0 4 3 0 2 2 1 0 1 0 0 2 = - = - = - = - = ∫∫ x x dx x x dx y y x dydx y x A Y X P x x ε (b) ( 5 points) Find the marginal p.d.f of X . Solution: 1 1 , 2 3 ) 1 ( ) 1 ( 2 3 |) | 1 ( 2 3 ) ( 2 0 1 1 0 2 1 1 2 < < - = - + + = - = - - x x dy y dy y x dy y x x f X III. ( 7 points) Let 40 2 1 , , , X X X denote a random sample of size 40 from the uniform distribution U(0,1). Find ). 7 . 11 5 . 8 ( X P

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quiz3AS-M1_f10 - Section M1 ECON 506 Section M1 Quiz 3...

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