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Unformatted text preview: = 0-Knowledge of X gives us full knowledge of Y , since Y is the square of X . However, their covariance is 0, because X 2 is a non-linear function of X Question 2 Assume E[u]=0. Show that E [ u | x ] = 0 Cov ( x,u ) = 0 Cov ( x,u ) = E [( x-E [ x ])( u-E [ u ])] 1 by E [ u ] = 0 then Cov ( x,u ) = E [ xu ] by the law of iterated expectations: = E [ E [ xu | x ]] Since x is now xed, = E [ xE [ u | x ]] = E [ x 0] = 0 2...
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- Fall '06