# hw1 - ECN 725 ASSIGNMENT 1 DUE February 4 (Thursday) S.C....

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ECN 725 ASSIGNMENT 1 S.C. AHN DUE February 4 (Thursday) Write your answers and derivation processes as clearly as possible. 1. (60 pts.) The joint probability distribution of X and Y is given by the following table: (For example, f(4,9) = 0.) x\y 1 3 9 2 1/8 1/24 1/12 4 1/4 1/4 0 6 1/8 1/24 1/12 (1) Find the marginal pdf of x . (2) Find f ( y | x ) for each x = 2, 4, 6. (3) Find E( y | x ) for each x . (4) Find var( y | x ) for each x . (5) Is there heteroskedasticity in y? Explain why or why not. (6) Compute R 2 . 2. (10 pts.) Suppose that (|) Eyx for all x , and () 0 Ex . Find the condition under which cov( , ) 0 xy . 3. (20 pts.) Consider two random variables X and Y which are correlated and normally distributed: 2 2 ~, x xx y y xy y X N Y     Let 2 2 2 1( ) (, , ) e x p 2 2 w ww w w w w    , which is the normal density function. Note that 2 Pr( ) ( , , ) 1 Ww d w       . Define 1 2 () xy yx x gx  , 2 2 2 2 xy yy x g . (1) (5 pts.)

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## This note was uploaded on 11/19/2010 for the course ECON 270a taught by Professor Ahn during the Spring '10 term at ASU.

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hw1 - ECN 725 ASSIGNMENT 1 DUE February 4 (Thursday) S.C....

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