Assignment 1 Answers

Assignment 1 Answers - ECON 425 Key for ASSIGNMENT 1 S. C....

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1 ECON 425 Key for ASSIGNMENT 1 S. C. Ahn 1. ( ) ( ) 1 .1 2 .2 3 .3 4 .4 0.1 0.4 0.9 1.6 3 yy Ey y f y   222 2 2 var( ) ( ) ( ) (1 3) 0.1 (2 3) .2 (3 3) .3 (4 3) .4 0.4 0.2 0.4 1 yyf y     2. (1) ( 2) 1/8 1/ 24 1/12 6 / 24 1/ 4; ( 4) 1/4 1/4 2/4 1/2; ( 6) 1/ 4 x x x fx ( 1) 1/8 1/4 1/8 1/2; ( 3) 1/24 1/4 1/24 1/3; ( 9) 1/12 0 1/12 1/6 y y y fy (2) X and Y are stochastically dependent. To show this, it is sufficient to show that for some x and y, f(x,y) f x (x)f y (y). For example, choose (x,y) = (4,9). Then, f(x,y) = 0; f x (x)f y (y) = (1/2)•(1/6) = 1/12. So, f(x,y) f x (x)f y (y). (3) ( ) ( ) 2 (1/ 4) 4 (1/ 2) 6 (1/ 4) 4; ( ) ( ) 1 (1/2) 3 (1/3) 9 (1/6) 18/6 3 xx x y Ex x f x y   (4) 22 2 2 2 2 var( ) (2 4) (1/4) (4 4) (1/2) (6 4) 2; var( ) (1 3) (1/2) (3 3) (1/3) (9 3) (1/6) 8. x y x y (5) ( 24 )( 13 1 / 8 33 1 / 2 4 93 1 / 1 2 ) 4) (1 3) (1/4) 4) (3 3) (1/4) 4) (9 3) 0 ( 64 1 / 8 1 / 2 4 1 / 1 2 ) 1/2 1 1/2 1 0 xy       0 (, ) 0 xy xy xy corr x y  (6) (2,9) 1 1 Pr( 2 | 9) ; Pr( 9 | 2) (9) 1/6 2 (2) 1/4 3 yx ff XY Y X Pr( 2 | 9) Pr( 9 | 2) YX . (7)
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Assignment 1 Answers - ECON 425 Key for ASSIGNMENT 1 S. C....

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