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# 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 y y E y yf y   2 2 2 2 2 var( ) ( ) ( ) (1 3) 0.1 (2 3) .2 (3 3) .3 (4 3) .4 0.4 0.2 0.4 1 y y y y f y   2. (1) ( 2) 1/8 1/ 24 1/12 6 / 24 1/ 4; ( 4) 1/ 4 1/ 4 2 / 4 1/ 2; ( 6) 1/8 1/ 24 1/12 1/ 4 x x x f x f x f x ( 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 f y f x f x (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 x x x y y y E x xf x E y yf y     (4) 2 2 2 2 2 2 2 2 var( ) (2 4) (1/ 4) (4 4) (1/ 2) (6 4) (1/ 4) 2; var( ) (1 3) (1/ 2) (3

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

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